Brown the Ground Beef: In a large saucepan, heat over medium-high heat and add the ground beef. Cook for 5–7 minutes until browned, stirring occasionally to break it up, and ensure there's no excess pink. Once it's browned, drain any fat and set the beef aside.

Sauté Vegetables: In the same saucepan, reduce the heat to medium and melt 2 tablespoons of butter. Add chopped onions, diced carrots, and celery, sautéing them for about 10 minutes until they are tender and fragrant. Stir in minced garlic and cook for another minute to enhance the flavors.

Combine Ingredients: Pour in 4 cups of chicken broth while stirring the sautéed vegetables. Next, add the diced peeled potatoes, stirring to combine everything well. Bring the mixture to a rapid boil, watching for bubbling and steam after a few minutes.

Simmer: Once boiling, reduce the heat to low, cover the saucepan, and let it simmer for 10–12 minutes. Check the potatoes for doneness; they should be fork-tender.

Make Roux: In a separate skillet, melt the remaining 2 tablespoons of butter over medium heat. Add in 1/4 cup of all-purpose flour, whisking constantly for about 2-3 minutes until the mixture bubbles and forms a roux.

Thicken Soup: Gradually introduce the roux into the simmering soup, stirring continuously to prevent lumps. Bring the soup back to a gentle boil for 2 minutes.

Add Dairy: Stir in 8 ounces of Pepper Jack Velveeta and 1 cup of milk into the thickened soup. Mix thoroughly until the cheese melts completely.

Finish: Remove the saucepan from heat and gently fold in 1/2 cup of sour cream. Stir well to combine all the elements.