Heat 2 tablespoons olive oil in a large pot or Dutch oven over medium heat. Add the leeks, salt, and several grinds of pepper. Sauté for 6 to 8 minutes, until softened.
Add the garlic, stir, and cook for 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, uncovered, for 30 minutes.
Let cool slightly, then transfer the soup to a blender with the remaining 1 tablespoon olive oil, the lemon juice, and the mustard. Blend until smooth. Work in batches if necessary. Season to taste and serve with chopped parsley, pine nuts, red pepper flakes, and drizzles of additional olive oil, if desired.