Heat one tablespoon olive oil in a large pot over medium-high heat. Add the capicola, red onion and minced garlic. Stir until the onion softens (for about 2 minutes). Add the carrots and celery thinly sliced. Cook stirring, until slightly softened. Add beans, tomatoes, two cups water, the parmesan rind, 1/2 teaspoon salt and a few grinds of pepper. Cover and cook until the vegetables are tender.
Meanwhile, lightly toast the bread, rubbing both sides with the whole garlic clove and sprinkle with grated Parmigiano Reggiano. Stir the escarole into the soup and cook until wilted. Top each serving of soup with a piece of toast. Drizzle with the remaining one tablespoon olive oil.