Gnocchi with Brown Butter and Sage

Put potatoes into a 4-qt. pot of salted water; boil. Reduce heat to medium-low; simmer until potatoes are tender, 25 minutes. Drain; let cool. Peel potatoes; pass through medium plate of a food mill into a bowl.

Meanwhile, heat a 12" skillet over medium-high heat. Add spinach and 1 tbsp. of water; cook until wilted. Press on spinach in a sieve to extract liquid. Finely chop spinach; stir together with potatoes and semolina and form a well in center. Add eggs and salt and, using a fork, beat eggs into potato mixture. Transfer dough to a work surface dusted with semolina; knead to combine. Divide the dough into 6 portions. Roll each portion into a 1⁄2"-thick rope. Cut ropes into 1⁄2"-wide pieces; transfer to semolina-dusted sheet tray.

Melt 10 tbsp. butter in a 10" skillet over medium heat; cook, swirling, until butter browns, about 6 minutes. Add sage and nutmeg; season with salt and pepper. Remove from heat; set aside.

Working in 4 batches, add 2 tbsp. butter and 1 tbsp. oil to a 12" skillet over medium-high heat. Add dough pieces and cook, flipping once, until golden brown, 3–4 minutes. Transfer to a baking sheet. Wipe out skillet and repeat with remaining butter, oil, and dough pieces. Toss dumplings and brown butter sauce in the skillet until hot. Serve sprinkled with Parmesan.