Preheat oven to 350◦. Thoroughly scrub the potatoes and pierce each several times with a fork. Place on a baking sheet and bake until the insides are tender, 1 1/2 - 2 hours. Let the potatoes cool until you can safely handle them, then peel and coarsely mash.
Melt the butter in a large pot over medium heat. Add the onion and cook, stirring occasionally, until softened, 8 - 10 minutes. Add the flour and stir to combine.
Whisk in the milk a little at a time, whisking between each addition until fully incorporated. Whisk in the broth, then increase the heat to medium high to bring to a boil. Reduce the heat to maintain a gentle simmer, and cook, whisking occasionally, until slightly thickened, 10 - 15 minutes.
Remove the pot from the heat and whisk in the sour cream, salt, and pepper. Gently stir in the mashed potatoes.