1 cup packed basil leaves
2 cloves garlic
6 Tbs. olive oil
3 Tbs. water; more or less as needed
1/2 cup grated Parmesan cheese
For the ragoût:
3 Tbs. extra-virgin olive oil
2 bay leaves
2 medium onions, cut into large chunks
7 plump cloves garlic, halved
3 sprigs fresh thyme
6 fresh sage leaves
3/4 lb. carrots, scrubbed, peeled if necessary, cut into 2 inch lengths (or baby carrots, left whole)
3/4 lb. small new potatoes, scrubbed
Salt and freshly ground black pepper to taste
1/2 lb. green beans, ends trimmed, halved crosswise
1 yellow bell pepper, cored, seeded, and cut into 1-inch pieces
1 lb. summer squash, cut into 1-inch rounds
5 plum tomatoes, peeled, seeded, and cut into large chunks
1 15-oz. can top-quality white beans, rinsed and drained (or about 2 cups cooked white beans)
Make the pesto: In a blender, process the basil and garlic with the oil, adding a little water to loosen if needed. Add the salt and the cheese, if using. Taste and adjust the seasonings if needed. Refrigerate until 30 minutes before using.
Make the ragoût: In a large flameproof casserole or Dutch oven with a snug lid, heat the oil with the bay leaves over low heat. When fragrant, add the onions, garlic cloves, thyme sprigs, and the sage, stirring to coat everything thoroughly with oil. Cover and cook over low heat as you prepare the rest of the vegetables. Add the carrots to the pot. If the potatoes are the size of large marbles, leave them whole, but quarter larger ones or cut fingerlings in half lengthwise. Add the potatoes to the pot in one layer; season with salt and pepper. Add the green beans, bell peppers, and summer squash to the pot in layers, seasoning each layer with a little salt and pepper as you go. Add the tomatoes, sprinkling their juices over all. Cover and cook over low heat until the vegetables are tender, 40 to 65 min. If tightly covered, the vegetables will produce plenty of flavorful juices. There's no need to stir, but if the pot seems dry, add a few tablespoons of water or dry white wine, if you like. Add the beans and cook until heated through, adding a little more water if needed.
Ladle the ragoût into soup plates, drizzle some pesto over each dish, and serve.