Pasta e Ceci (Pasta with Chickpeas)

Process pancetta in food processor until ground to paste, about 30 seconds, scraping down sides of bowl as needed. Add carrot, celery, and garlic and pulse until finely chopped, 8 to 10 pulses. Add onion and pulse until onion is cut into 1/8- to 1/4-inch pieces, 8 to 10 pulses. Transfer pancetta mixture to large Dutch oven. Pulse tomatoes in now-empty food processor until coarsely chopped, 8 to 10 pulses. Set aside.

Add oil to pancetta mixture in Dutch oven and cook over medium heat, stirring frequently, until fond begins to form on bottom of pot, about 5 minutes. Add anchovy, pepper flakes, and rosemary and cook until fragrant, about 1 minute. Stir in tomatoes, chickpeas and their liquid, water, and 1 teaspoon salt and bring to boil, scraping up any browned bits. Reduce heat to medium-low and simmer for 10 minutes. Add pasta and cook, stirring frequently, until tender, 10 to 12 minutes. Stir in lemon juice and parsley and season with salt and pepper to taste. Serve, passing Parmesan and extra oil separately.