Cook the pancetta in a large soup pot over medium heat for 6 to 8 minutes, until crisp. Remove with a slotted spoon, setting aside about half for topping.
Add the onion, carrot, and celery to the pot. Cook for 6 to 7 minutes, until softened.
Add the garlic and cook for 1 minute, until fragrant.
Stir in the beans, stock, and bay leaf. Bring to a simmer and cook for 20 to 25 minutes.
Stir in the remaining half of the pancetta and the kale. Cook for 3 to 4 minutes, until wilted. Season with salt and pepper.
While the soup simmers, combine the parsley, capers, garlic, vinegar, and olive oil in a food processor. Pulse until finely chopped. Season with salt.
Remove the bay leaf. Ladle the soup into bowls and top each with the reserved crispy pancetta and a spoonful of salsa verde.