Place the potatoes, onion, celery, basil, parsley, chicken broth, and tomatoes in a slow cooker. Cook on low for 8 hours or high for 4 hours.
Thirty minutes before you're ready to eat, brown the ground beef in a skillet. Drain any excess fat, then add the ground beef to the crock pot. (If you're cooking the bacon, add it to the skillet and fry while you proceed with the recipe. When crisp, remove from the skillet and drain on paper towels).
Whisk together the cornstarch and 1/4 cup of the milk until smooth. Stir it into the slow cooker, then add the remaining milk, cheddar cheese, and sour cream, stirring to combine. Turn the slow cooker up to high and cook for another 10-15 minutes or until soup is slightly thickened and heated through. Season to taste with salt and pepper.
In the meantime, preheat the oven to 450 degrees and bake the tater tots according to package directions.
Serve the soup warm topped with tater tots, bacon, and green onions, if desired.