Heat 1 tablespoon olive oil in a large heavy-bottomed pot over medium-high heat. Add the capicola, red onion and minced garlic. Cook, stirring, until the onion softens, about 2 minutes. Add the carrots and celery. Cook, stirring, until slightly softened, about 5 minutes. Add the beans, tomatoes, 2 cups water, the parmesan rind, 1/2 teaspoon salt and a few grinds of pepper. Bring to a simmer, then cover and cook until the vegetables are tender, 15 to 20 minutes. Remove the parmesan rind.
Meanwhile, lightly toast the bread; rub both sides with the whole garlic clove and sprinkle with grated parmesan. Stir the escarole into the soup and cook, stirring occasionally, until wilted, about 5 minutes. Top each serving of soup with a piece of toast. Drizzle with the remaining 1 tablespoon olive oil.