In a 3-quart saucepan, heat over medium-high heat and add lean ground beef. Cook until browned, about 5-7 minutes. Drain excess fat and set aside.

In the same saucepan, melt butter over medium heat. Add chopped onion, shredded carrots, and diced celery; sauté for about 10 minutes until the vegetables are tender.

Stir in minced garlic and cook for an additional minute until fragrant.

Pour in the chicken broth, stirring in the diced potatoes and the cooked beef. Bring to a boil, then reduce heat.

Cover and let the soup simmer for 10-12 minutes or until the potatoes are fork-tender.

In a small skillet, melt remaining butter over medium heat. Whisk in flour for about 2 minutes until bubbly.

Stir the roux into the simmering soup. Increase heat and cook for another 2 minutes.

Reduce heat and add in the Pepper Jack Velveeta cheese, milk, salt, and black pepper. Stir until the cheese melts.

Remove from heat and stir in the sour cream until fully combined.