In a large pot, cook the ground beef over medium heat for about 6-8 minutes, crumbling it as it cooks. Drain any excess fat.
Add 1 tablespoon of butter to the pot and sauté the onion, carrots, and celery for about 10 minutes until tender.
Stir in the potatoes, chicken broth, basil, and parsley. Bring to a boil, then reduce heat and simmer for 10-12 minutes until potatoes are tender.
In a small skillet, melt the remaining butter and whisk in the flour. Cook for 3-5 minutes until bubbling, then stir into the soup.
Bring the soup back to a boil and then reduce heat. Stir in the Velveeta cheese, milk, salt, and pepper until the cheese is melted and the soup is creamy.
Remove from heat and stir in the sour cream. Serve hot, garnished with onion rings and green onions if desired.
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Notes
Store leftovers in an airtight container in the refrigerator for up to 3-4 days.