In a large pot, cook the ground beef over medium heat until browned. Drain excess fat and set the beef aside.
In the same pot, melt 1 tablespoon of butter and sauté the onion, carrots, celery, basil, and parsley until the vegetables are tender.
Pour in the chicken broth, add the diced potatoes, and return the cooked beef to the pot. Bring to a boil, then reduce heat, cover, and simmer until the potatoes are tender, about 10 to 12 minutes.
In a separate small skillet, melt the remaining 3 tablespoons of butter and whisk in the whole-wheat flour. Stir continuously for 3 to 5 minutes until the mixture is bubbly. Add this thickener to the soup, bring to a boil, and cook for 2 minutes while stirring. Then, reduce the heat to low.
Add the shredded cheddar cheese, milk, salt, and pepper to the soup. Continue to cook and stir until the cheese is completely melted. Remove from heat and stir in the Greek yogurt until well combined.
