Cook the bacon strips in a large pot over medium heat until crispy, about 8-10 minutes, stirring occasionally. Remove the bacon to a paper towel-lined plate and crumble it once cooled, reserving about 2 tablespoons of the rendered fat in the pot. While the bacon cooks, dice the onions into small, uniform pieces and mince the garlic cloves—this ensures they'll cook evenly and integrate smoothly into the soup base.
Add the butter to the reserved bacon fat in the pot and let it melt over medium heat. Stir in the diced onions and cook for 4-5 minutes, stirring occasionally, until they become translucent and softened. Add the minced garlic and cook for about 30 seconds until fragrant. Sprinkle in the flour and stir constantly for 30 seconds to cook out the raw flour taste—this creates the roux that will thicken the soup and give it a silky texture.
Gradually whisk in the chicken stock and milk, stirring constantly to avoid lumps and ensure the roux incorporates smoothly. Bring the mixture to a gentle simmer, then add the cubed red potatoes. Add the salt, pepper, smoked paprika, and cayenne pepper, stirring to combine. I like to add the spices early so they distribute evenly throughout the broth and develop more flavor as everything simmers together.
Maintain a gentle boil and cook for 10-15 minutes, stirring occasionally, until the potatoes are fork-tender but still holding their shape. The timing depends on how small you cut them—smaller pieces cook faster. Once the potatoes are done, reduce the heat to low; this prevents the soup from breaking or the potatoes from becoming mushy.
Remove the pot from heat and stir in the freshly shredded cheddar cheese until completely melted and incorporated. Fold in half of the crumbled bacon from Step 1. I always shred the cheese fresh rather than using pre-shredded, as it melts much more smoothly and gives the soup a creamier finish without any graininess.
Ladle the soup into bowls and top each serving with a dollop of sour cream, the remaining crumbled bacon, and a generous handful of thinly sliced green onions cut on the bias. The bias cut makes them look elegant and helps them distribute better across the surface.