Bucatini Pasta with Pork Ragu

Name: Bucatini Pasta with Pork Ragu
Ingredients: 1/4 cup extra virgin olive oil; 1 pound ground pork; 1 pound sweet Italian sausage; 4 ounces pancetta or bacon (optional, but recommended); 1 large carrot; 2 celery ribs; 1 medium onion (or half a large one); 4 large garlic cloves (or more if they are small); 1/4 cup plus 2 tablespoons chopped fresh parsley; 1 tablespoon chopped fresh oregano (or 1/2 tablespoon dry oregano); 2 to 3 anchovies; 2 dry hot Calabrian chile peppers, crumbled (or 1/4 teaspoon regular hot pepper flakes); 1 tablespoon tomato paste (preferably Italian, from San Marzano tomatoes); 28 ounces can of San Marzano tomatoes (can use regular, but it won't be the same!); 1/4 cup dry red wine; 1 pound bucatini pasta; 1/2 cup grated fresh Parmesan cheese (plus more for serving); 1/3 cup grated fresh pecorino cheese (can just use Parmesan if not available; just add an extra 1/3 cup); 2 or more cups water; Kosher salt and freshly ground black pepper to taste; Very high quality balsamic vinegar to taste (optional)