Step 1

Preheat the oven to 375°. In a large enameled cast-iron casserole, heat 2 tablespoons of the olive oil. Rub the pork all over with the remaining 2 tablespoons of olive oil and season with salt and pepper. Add to the casserole and cook over moderately high heat until browned all over, about 8 minutes; transfer to a plate. Add the garlic to the casserole and cook, stirring, until golden, 1 to 2 minutes. Add the wine; cook until almost evaporated, about 2 minutes.

Step 2

Add the milk, rosemary sprigs, bay leaf and lemon zest to the casserole and bring to a simmer. Add the pork and braise in the oven for about 3 hours, until the meat is very tender. Let the pork cool in the casserole to room temperature.

Step 3

Transfer the pork to a work surface and cut in half. Coarsely chop 1 piece; reserve the remaining pork for another use. Working in 2 batches, puree the cooking liquid in a blender until smooth. Strain through a fine sieve, pressing down on the solids.

Step 4

Preheat the oven to 425°. Lightly grease a 3½- to 4-quart baking dish. In a pot of salted boiling water, cook the pasta until very al dente. Drain and transfer to a large bowl. Add the chopped pork and 3 cups of the strained cooking liquid, season with salt and pepper and toss to coat. Transfer the pasta to the prepared baking dish and dollop the ricotta on top. Cover with foil and bake for about 20 minutes, until the pasta is tender. Uncover and bake for about 15 minutes longer, until golden on top. Garnish with pepper and chopped rosemary. Serve with grated pecorino.