Cover potatoes with water in a large pot; boil 15 minutes until fork-tender, drain, and set aside.
Melt butter in same pot over medium; whisk in flour and cook 2 minutes, stirring constantly, to form a roux.
Gradually whisk in milk and broth continuously to avoid lumps; simmer gently.
Return potatoes; mash about half with a potato masher, leaving chunks for texture.
Stir in cheddar until melted and smooth; season with salt and pepper.
Off heat, stir in sour cream and half the bacon.
Serve hot topped with remaining bacon, green onions, extra cheese, and more sour cream if desired.