Dice the onions, carrots, and celery. Grate the cheddar cheese, and cube the Velvetta.
In a heavy large dutch oven or large soup pot over medium heat, melt butter, salt, and pepper. Saute onions, carrots and celery until tender 5 minutes.
Stir in flour and cornstarch, cook another 3 minutes. Add chicken stock bone broth (or chicken broth) and heavy whipping cream gradually, blending until smooth about 3-5 minutes.
Turn heat down to medium-low, don’t allow soup to boil at any point. Add cubed Velveeta cheese and grated cheddar cheese, stir until melted, about 5 minutes. Add parsley, cayenne, and paprika.
Using an immersion blender (stick blender), mix the soup until smooth and creamy. Or blend in a blender in small batches, and be careful it's hot!
Simmer on medium-low heat for 20 minutes until it thickens. Serve in bowls or mugs with bread or croutons. Cool these delicious soup leftovers, and keep in an airtight container in the fridge until ready to reheat.