Heat your Dutch oven over medium-high heat and add the ground beef, breaking it into small pieces with your wooden spoon. Cook for 6 to 8 minutes, stirring occasionally, until the meat is browned and no pink remains. Transfer the beef to a plate and drain all but one tablespoon of fat from the pot.

Add 2 tablespoons of butter to the pot and let it melt over medium heat. Add the diced onion, celery, and carrots, stirring to coat them in the butter, and cook for 5 to 6 minutes until softened.

Add the minced garlic to the vegetables and cook for exactly 30 to 60 seconds, stirring constantly. The garlic should become fragrant but never brown.

Add the diced potatoes to the pot along with the chicken broth, stirring to combine everything evenly. Bring the mixture to a boil, then reduce heat to medium-low and simmer for 12 to 15 minutes until potatoes are tender.

While the potatoes simmer, melt the remaining 2 tablespoons of butter in a small saucepan over medium heat. Whisk in the flour and cook for 1 to 2 minutes, stirring constantly, until the mixture turns slightly golden and smells nutty.

Slowly pour the milk into the roux while whisking constantly to prevent lumps from forming. Continue whisking over medium heat until the mixture thickens enough to coat the back of a spoon, about 3 to 4 minutes.

Pour the thickened milk mixture into the pot with the potatoes and broth, stirring well to combine completely. Add the browned beef back to the pot and stir everything together.

Stir in the yellow mustard, Worcestershire sauce, and smoked paprika until evenly distributed. Taste the soup and add salt and pepper as needed.

Reduce heat to low and add the cubed Velveeta to the soup, stirring gently and continuously until it melts completely, about 2 to 3 minutes.

Remove the pot from heat entirely before adding the shredded cheddar. Add the cheese in three additions, stirring until each addition melts completely before adding more.

Stir in the sour cream until completely incorporated. Taste one more time and adjust salt and pepper if needed.

Let the soup rest for 5 minutes off the heat before serving. Ladle into bowls and top with bacon bits, diced pickles, chives, and extra cheese.