Heat 2 tablespoons of the olive oil in a large pot or Dutch oven over medium heat. Add the onion, salt, and several grinds of pepper. Sauté 6 to 8 minutes, until softened.

Add the garlic, stir, and cook 2 more minutes. Stir in the white wine vinegar and cook, stirring, for 30 seconds, and then add the broth, potatoes, and white beans. Bring to a boil, reduce the heat, and simmer for 30 minutes.

Let cool slightly, then transfer half of the soup to a blender with the remaining 1 tablespoon olive oil, the mustard, lemon juice, and paprika. Blend until smooth and return the pureed soup back to the pot.

Use a potato masher to gently smash the potato chunks and beans. Season to taste with more salt and pepper and serve with desired toppings.