In a food processor, place the pancetta and puree, about 30 seconds, scraping down sides when necessary.
Place the chopped carrot, celery, and garlic cloves in the processor with the pancetta and pulse 8 to 10 times.
Add the chopped onion and pulse again until finely minced.
Place the pancetta and vegetables in a dutch oven or other 6-quart stock pot and add the olive oil. Cook the olive oil and pureed mixture on medium heat, stirring occasionally for 5 minutes. Then, add the anchovy paste, rosemary, and pepper flakes and cook another minute.
While the vegetables cook, place the drained whole tomatoes in the food processor and pulse until finely chopped, but not pureed.
Next, add the chopped tomatoes, chickpeas, and their liquid, water, and salt, and bring to a boil. Reduce heat and simmer for 10 minutes.
Add pasta and cook until softened, about 11 minutes
Remove from the heat and stir in the lemon juice and parsley.
Serve hot with grated parmesan and more parsley if desired.