Peel and dice the potatoes into 1/2-inch cubes, keeping them in a bowl of cold water to prevent browning. Finely dice the onion, mince the garlic, and measure out all remaining ingredients into small bowls for easy access. Cook the bacon in a large pot over medium-high heat until crisp, about 8-10 minutes, then remove it to a paper towel. Crumble the bacon once cooled and set aside. Pour off all but 2 tablespoons of bacon grease from the pot, leaving just enough to flavor the aromatics—this is the foundation of your soup's depth.
Add the diced onion to the pot with the bacon grease and cook over medium heat for about 5 minutes, stirring occasionally, until softened and translucent. Add the minced garlic and butter, cooking for just 1 minute until fragrant—don't let the garlic brown or it will turn bitter. Sprinkle the flour over the mixture and stir constantly for 1 minute to cook out the raw flour taste. This roux will thicken your soup and create a silky, luxurious base.
While the roux is cooking, place the drained diced potatoes in a separate pot of salted water and bring to a boil over high heat. Simmer for about 15-20 minutes until the potatoes are very tender and easily pierced with a fork. The timing should align so they're done around the same time you finish the roux and sauce base. I find that cooking potatoes separately and then adding them keeps the soup broth clearer and the potatoes from becoming too starchy and thick.
Gradually whisk the broth into the roux mixture from Step 2, stirring constantly to prevent lumps from forming. Once smooth, add the cream and bring the mixture to a gentle simmer over medium heat, stirring occasionally for about 3-5 minutes until it thickens slightly and the flavors meld. The soup should coat the back of a spoon lightly but still flow freely.
Drain the cooked potatoes from Step 3 and add them to the creamy broth from Step 4, stirring gently to combine. Stir in the sour cream until fully incorporated, then season with salt, pepper, and smoked paprika. Taste and adjust seasonings as needed—I like to add the smoked paprika gradually since a little goes a long way. If you prefer a smoother soup, this is the time to use an immersion blender on just a few pulses for a rustic texture, or blend it fully for a completely smooth consistency.
Remove the pot from heat and stir in the shredded cheddar cheese until completely melted and smooth. Ladle the soup into bowls and top each serving with a generous handful of crumbled bacon from Step 1, fresh chives, and an extra pinch of cheese if desired. The residual heat will keep everything warm and creamy without any risk of the cream breaking.