Halve leeks lengthwise and cut crosswise into 1/2-inch pieces, then wash well and pat dry.
Cook leeks, carrots, celery, and garlic in oil with herb sprigs, bay leaf, cloves, and 1/2 teaspoon each of salt and pepper in a large heavy pot over medium heat, stirring occasionally, until softened and golden, about 15 minutes. Stir in beans, then water, and simmer, partially covered, stirring occasionally, until carrots are tender but not falling apart, about 30 minutes.
Make garlic crumbs while cassoulet simmers:
Preheat oven to 350°F with rack in middle.
Toss bread crumbs with oil, garlic, and 1/4 teaspoon each of salt and pepper in a bowl until well coated. Spread in a baking pan and toast in oven, stirring once halfway through, until crisp and golden, 12 to 15 minutes.
Cool crumbs in pan, then return to bowl and stir in parsley.
Discard herb sprigs and bay leaf. Mash some of beans in pot with a potato masher or back of a spoon to thicken broth. Season with salt and pepper. Just before serving, sprinkle with garlic crumbs.