Preheat the oven to 400ºF.
Melt butter in a large saucepan over medium heat. Add the leeks and ½ teaspoon of salt and cook, stirring occasionally, until soft, about 4 minutes.
Add garlic and cook until fragrant, 15 to 30 seconds. Stir in potatoes, cannellini beans, Parmesan Stock, and the remaining ½ teaspoon of salt. Reduce heat to low and simmer for 18 to 20 minutes.
Place the baguette on the wire rack in the oven and toast for 7 to 9 minutes, until the crust is crisp and the bread is warmed through.
Transfer soup to a blender or use an immersion blender to blend until smooth (see Note). Stir in heavy cream and black pepper. Taste and season with additional salt, if needed.
Ladle the soup in 2 to 4 bowls and top each bowl with 1 to 2 teaspoons of Lemon Salsa Verde. Serve with a crispy baguette on the side for dipping
