Scoop the flesh of the potatoes into a bowl and set aside. Discard the skins.
Melt butter in the pot and saute the white part of the onions and garlic for about 1 minute. Add flour and whisk constantly until the flour and butter mixture thickens and forms a light roux. The roux should have a slightly nutty taste, with no hint of flour. Watch carefully and do not over cook the roux.
Gradually whisk in the milk a cup at a time. Cook over medium-low until thickened and hot. Raise the heat as necessary, but watch it closely to make sure the milk doesn’t boil.
Add the potatoes, using a potato masher or stick blender to mash the large chunks. Stir to distribute the potatoes throughout the soup. Add the salt, black pepper, and paprika and stir.
Add ½ cup bacon bits, the sour cream, and the cheese. Stir until cheese is melted and thoroughly incorporated into the soup. Cook over medium-low until hot.
Pour into bowls and garnish with more bacon bits, scallions, and shredded cheese.