Dice 4 medium yellow onions (about 4 1/2 cups). Peel, core, and finely dice 2 medium apples (about 3 cups). Mince or grate 4 garlic cloves (about 1 tablespoon). Finely chop the leaves from 1 bunch fresh parsley until you have 1/2 cup. Finely grate 4 ounces Parmesan cheese (about 1 cup).

Heat 2 tablespoons olive oil in a large, heavy-bottomed pot such as a Dutch oven over medium-high heat until shimmering. Remove the casings from 12 ounces uncooked Italian sausage if needed, then add the sausage to the pot. Cook, breaking up the meat with a wooden spoon, until well-browned, 8 to 10 minutes. Using a slotted spoon, transfer the sausage to a bowl.

Add 4 tablespoons unsalted butter to the pot. When melted, add the onions, apples, 1 teaspoon dried thyme, 1/4 teaspoon red pepper flakes, 1 teaspoon kosher salt, and 1 teaspoon black pepper. Cook, stirring often to prevent the bottom from burning, until the onions are dark brown and the apples are very soft, 25 to 30 minutes. The onions should be the color of light mahogany wood. If the bottom of the pot starts to burn before the onions have fully caramelized, add 2 tablespoons of water to the pot, stir to help dissolve any burnt bits, and continue cooking. (Feel free to do this several times during cooking.)

Meanwhile, bring a large pot of heavily salted water to a boil. Add 1 pound dried orecchiette pasta and cook 2 minutes less than al dente, about 8 minutes or according to package instructions. Reserve 1 cup of the cooking water. Drain the pasta and set aside.

When the onions are ready, add the garlic and cook just until fragrant, 1 minute. Add 1 cup dry white wine, scrape up any brown bits from the bottom of the pot, and cook until the wine is completely evaporated, 4 to 7 minutes.

Add the pasta and 1/2 cup of the reserved pasta water. Cook until the water is completely absorbed by the pasta, 1 to 3 minutes. The pasta should look very glossy and saucy. If it looks dry, add more pasta water a tablespoon at a time as needed (you might not use all the remaining pasta water).

Remove the pot from the heat. Return the cooked sausage and any accumulated juices, half the parsley, and half the Parmesan to the pot and stir to combine. Serve immediately, garnishing each portion with the remaining parsley and Parmesan.