Prep the Meat:
In a skillet over medium heat, brown the ground beef with the diced onion and minced garlic until the meat is no longer pink and the onions are translucent. Drain any excess fat.
Season the beef with salt, pepper, and paprika. Transfer the mixture to the slow cooker.
Add Vegetables and Broth:
To the slow cooker, add the chicken or beef broth, canned diced tomatoes, diced potatoes, carrots, and celery. Stir to combine.
Cook the Soup:
Cover the slow cooker and cook on low for 6-7 hours or on high for 3-4 hours, until the vegetables are tender.
Add Dairy Ingredients:
About 30 minutes before serving, if you prefer a thicker soup, whisk the flour into the heavy cream until smooth, then stir this mixture into the soup. If you don’t need to thicken the soup, simply stir in the heavy cream.
Add the shredded cheddar cheese and stir until melted and well incorporated.
Finish with Sour Cream:
Just before serving, stir in the sour cream for extra creaminess and adjust the seasoning if necessary.
Serve:
Ladle the soup into bowls.
Garnish with additional shredded cheese, diced pickles, and tomatoes if desired.