Step 1

Heat oil in a large Dutch oven over medium. Add pancetta; cook, stirring often, until fat has rendered, about 5 minutes. Using a slotted spoon, transfer pancetta to a plate, reserving drippings in Dutch oven. Add garlic to Dutch oven; increase heat to medium-high. Sprinkle chicken all over with salt and pepper. Working in batches if needed, add chicken, skin side down, to Dutch oven. Cook until golden brown on both sides, about 6 minutes. Transfer chicken thighs to a plate.

Step 2

Reserve garlic and 2 tablespoons drippings in Dutch oven; discard remaining drippings. Add sofrito and wine; bring to a simmer over medium. Cook, stirring and scraping up browned bits, until mixture is reduced by half, about 3 minutes. Return chicken to Dutch oven in a snug single layer; add stock, ensuring chicken is barely covered. Return mixture to a simmer over medium. While mixture comes to a simmer, bundle together leek leaves, rosemary sprigs, thyme sprigs, and bay leaf; secure with kitchen twine, and add to Dutch oven. Reduce heat to medium-low; cover and cook until chicken is tender, 45 minutes to 1 hour.

Step 3

Remove Dutch oven from heat. Transfer chicken to a cutting board; partially cover Dutch oven. Let chicken and sauce stand 10 minutes. Skim and discard fat from sauce; remove and discard garlic cloves and leek-herb bundle. Stir reserved pancetta into sauce. Remove and discard skin and bones from chicken; finely shred chicken meat.

Step 4

Stir cream into sauce. Cook over medium-high, stirring occasionally, until sauce is reduced by nearly half and has slightly thickened, 8 to 12 minutes. Stir peas and shredded chicken into sauce; cook until peas are just tender, about 2 minutes. Season with salt and pepper to taste. Remove from heat, and cover to keep warm.

Step 5

Cook pasta according to package directions; drain pasta, reserving 1/2 cup cooking liquid.

Step 6

Add pasta, Parmesan, butter, and lemon zest to sauce. Stir to combine, adding splashes of reserved cooking liquid as needed to form a creamy sauce. Sprinkle with parsley. Serve in large bowls.