Sweet Corn and Ricotta Raviolo

Cook corncobs in a large pot of boiling salted water until softened, 45–60 minutes. Discard cobs; let broth sit at room temperature until ready to use.

Meanwhile, heat 3 Tbsp. butter in a large skillet over medium-high. Cook corn kernels, shallot, garlic, 1 tsp. salt, and ¼ tsp. pepper, stirring occasionally, until vegetables are tender and juices have evaporated and browned on bottom of pan, 10–12 minutes. Transfer to a medium bowl.

Add wine to skillet and cook, scraping up browned bits, until syrupy, about 2 minutes. Scrape into corn mixture, toss gently to combine, and let cool slightly. Stir ricotta and chopped basil into corn mixture; taste and season with salt and pepper if needed. Cover and let sit at room temperature until ready to use.

Dust a large rimmed baking sheet with cornmeal. Set pasta maker to thickest setting; dust lightly with cornmeal. Divide dough into 5 pieces. Working with 1 piece at a time and keeping remaining dough wrapped in plastic as you work, flatten dough into a narrow rectangle (no wider than mouth of machine); pass through rollers. Fold dough as needed to fit and roll again. Repeat without folding, adjusting machine to thinner settings after every pass and dusting with cornmeal if sticky, until pasta is 1/16" thick (setting 8 on most machines). (Alternatively, you can roll out sheets lengthwise with a rolling pin until 1/16" thick.)

Lightly dust work surface with cornmeal. Working with 1 length at a time and keeping remaining dough wrapped in plastic as you work, cut dough in half crosswise. Starting 3" from the short edge, spoon 2 Tbsp. corn mixture onto 1 strip. Spoon second mound 4" away from first. Using the back of a tablespoon, create a divot in both mounds. Carefully slip 1 egg yolk into each depression. Top each yolk with 1 basil leaf. Lightly brush egg wash around each mound. Top with second dough strip; use fingertips to press dough around each mound to seal, then firmly press outward toward edges to push out any air pockets.

Cut out each ravioli with cookie cutter. Transfer to prepared sheet, dust with cornmeal, and cover loosely with plastic wrap. Repeat with remaining dough and filling.

Return corn broth to a boil. Working in 2 batches, cook ravioli, stirring occasionally, 2 minutes (ravioli will be slightly undercooked; they will continue to cook in the sauce). Using a slotted spoon, transfer ravioli to a plate.

Transfer 1 cup pasta cooking liquid to a large skillet. Bring to a boil; add ravioli and remaining 3 Tbsp. butter. Cook, gently spooning sauce over ravioli, until sauce thickens slightly, 1–2 minutes.

Divide ravioli among plates. Drizzle with oil, top with Parmesan, and season with pepper.

Do Ahead: Corn mixture can be made 1 day ahead. Cover and chill.