Homemade Coquito (Puerto Rican Eggnog)

Heat oven to 400°. Using a corkscrew, open the three "eye" holes at the narrow end of each coconut; invert over a measuring cup fitted with a fine mesh strainer. Drain coconuts, reserving liquid; set aside. Bake coconuts 20 minutes; transfer to a cutting board, cover with a towel and tap sharply with a hammer until coconuts crack into large pieces. With a paring knife or large spoon, remove meat from shell; peel away brown papery husk and discard. Finely chop meat (you should have about 4 cups); set aside.

Combine reserved coconut liquid and enough water to equal 2 cups; add cinnamon stick, star anise, and anise seeds. Bring to a boil in a 1-qt. saucepan over medium-high heat; reduce heat to medium and cook 5 minutes. Remove from heat and steep 10 minutes. Strain and discard spices; set aside.

Combine liquid and half of coconut meat in a blender; mix on high speed until finely pureed and thickened, about 30 seconds. Pour through a cheesecloth-lined fine mesh sieve into a measuring cup; gather ends of cheesecloth, twisting tightly to extract liquid. Discard coconut solids and return strained liquid to blender with remaining coconut meat. Repeat blending and straining process (you should have 2-3 cups coconut milk); rinse blender and wipe dry.

Combine coconut milk, yolks, condensed milk, evaporated milk, cinnamon, nutmeg, and salt in blender; mix on high speed until frothy, 30-60 seconds. Whisk in rum and refrigerate until ready to use.