His notion was old-fashioned (this was 1964)—as was his ingredient list (he lists shortening in lieu of butter), but the lure of this Hungarian classic transcends time.

Unlike Hungary’s humble national dish guylas (or to Americans, goulash), paprikás csirke has had its fair share of opulent moments. Though the dish is categorically babushka-esque (born of Hungarian grandmothers), chicken paprikash grew to fame when noted French chef Georges Auguste Escoffier put poulet au paprika and gulyas hongroise on the menu at the Grand Hotel in Monte Carlo in 1879, a century before Pasternak started serving it to the Hollywood set.

But you need neither fame nor fortune to master a decadent-feeling chicken paprikash: It starts with chicken pieces dredged, browned, doused with paprika, and slowly simmered in water or broth, before a sour cream roux is added, creating a fragrant (and impossibly easy) gravy.

The classic Hungarian cookbook Kis Magyar Szakácskönyv, published in 1934, approaches chicken paprikash more as a preparation, than a prescribed dish, listing chicken, pork, or game equally, with directions for dredging, searing, and simmering the paprika gravy to serve on top—no matter which protein you choose.

In Hungary, chicken paprikash is most often served with homemade egg noodles, called csipetke (which literally translates to “pinched dumplings”) or tojásos galuska (egg dumplings)—Hungary’s answer to chicken and dumplings. Like its American counterpart, the simple chicken gravy of old was enriched with the addition of aromatics and paprika (thanks to the arrival of nightshades from the New World in the late 15th century); peppers, onions, and tomatoes have become an integral part of today’s classic chicken paprikash—while the dumplings themselves have stayed steady in their simplicity.

Csipetke are well worth learning to make; simpler than gnocchi or other handmade pastas, a basic egg, flour, and water dough (with salt for flavor) is stirred together, rested, and kneaded, or often rolled, before being pinched off and cooked in boiling water. While they resemble nokedli, the Hungarian equivalent of German spaetzle (in which a wettish batter gets forced through a sieve or noodle grater), the only technique here is to pinch and roll dough between the fingers. Even children can make them (and in Hungary, children often do). You can embellish them with a final sauté in butter and parsley, or serve them simply boiled, paprika gravy spooned alongside.

Whether it's served with or without noodles, Hungarians almost always garnish chicken paprikash with rings of green pepper, in typical, no-fuss fashion. In matters of food, most Magyars weigh virtue over beauty—and for this dish in particular, I’m fully on board. Here’s how to get this comfort food just right.

Before you get started in on the chicken, set yourself up to make dumplings. Bring a large pot of salted water to a boil. Meanwhile, make the dumpling dough by stirring together the flour and salt. Make a well in the center of the dry ingredients, and like when making pasta, add the egg right into the well.

Add in ½ cup of water and stir together, with your fork or fingers, into a shaggy dough. Knead inside your bowl or on a lightly floured surface until smooth, about a minute.

To keep the dumplings tender, use your fingers or a teaspoon to scoop walnut-size pieces of dough from the bowl straight into the pot, one by one. Boil the dumplings until they float to the top and are tender (test one, cooling it well on a spoon first), about 6 to 8 minutes. You can drain the dumplings in one fell swoop, and rinse them in cold water to stop the cooking—or you can cook them in batches, and reheat them in the pot below. Just don’t let them overcook.

At this point, your chicken should already be resting at room temperature. Season it well with salt and pepper, and dredge it lightly in flour (a shallow plate filled with flour works well for this, since you can dump the flour and wash the dish later). Heat a large Dutch oven over medium-high and add the oil. Add the chicken, skin-side down, then cook, turning once, until brown on all sides, 8 to 10 minutes. Pull from the pot and set aside on a clean plate.

Next add your paprika and half the peppers, plus the tomatoes and onions to the fat in the pot. Cook, stirring to keep the mixture from browning, until the onions are soft, about 5 minutes. Return the chicken to the pot, along with the broth and bring it all to a boil. Reduce the heat to a simmer and cook, covered, turning once, until the chicken is just cooked through, about 15 minutes.

To make the gravy, whisk together the remaining flour and sour cream in a bowl. Pull about ¾ cup of broth from the pot and whisk it gradually into the sour cream roux until smooth. Return the roux to the pot of simmering chicken and broth, and stir to bring it all together. Simmer a few minutes more to cook out the flour taste, then remove from the heat, or turn down to low to keep warm.

At this point, your chicken and dumplings are both fully cooked. For the finishing touch, melt butter in a large skillet over medium-high heat and add the dumplings, cooking to brown lightly and heat through, 1 to 2 minutes. Add the parsley and toss with the dumplings (you want the parsley to stay green but still feel integrated with the dumplings, which should be comforting and warm).

To serve, transfer the dumplings to a bowl and the chicken and gravy to a platter, and garnish with the remaining fresh green pepper. Or serve a few dumplings on each plate, with chicken and paprika gravy over the top.