Prick the potatoes with a fork and bake them at 400°F for 45 to 50 minutes until soft. Let them cool slightly, then scoop out the flesh and set it aside.
In a large pot over medium heat, cook the diced onion for 5 minutes until it softens. Add the minced garlic and cook for 1 minute more.
Pour in the chicken broth and add the white beans along with the scooped potato flesh. Bring the mixture to a simmer and cook for 10 minutes.
Use a potato masher to break down some of the potatoes and beans for a thicker texture. Stir in the milk and let the soup heat through for 3 minutes.
Remove the pot from the heat and stir in half of the shredded cheddar cheese until it melts. Season with salt and black pepper to taste.
Ladle the soup into bowls and top each serving with the remaining cheddar cheese, crumbled bacon, and sliced green onions.