Brown the ground beef in olive oil in a large pot or Dutch oven over medium heat. Drain off any excess grease.
Add the chopped onion and celery to the pot with the beef. Cook until the vegetables soften, about 5 to 7 minutes.
Stir in the beef broth, Dijon mustard, Worcestershire sauce, garlic powder, and onion powder. Bring the mixture to a simmer.
Reduce the heat to low. Add the cubed cream cheese, stirring constantly until it melts completely and the soup base is smooth. Do not let it boil after adding the cream cheese.
Stir in the heavy cream. Continue to heat gently until the soup is hot throughout.
Remove the pot from the heat. Gradually stir in the cheddar cheese and Monterey Jack cheese until fully melted and incorporated, creating a creamy texture.
Season with salt and pepper to your preference.
Ladle the soup into bowls and add your desired toppings.
Notes
For a smoother texture, you can use an immersion blender briefly after the cheese melts, but avoid over-blending.
If you need to substitute Worcestershire sauce, use 1/2 teaspoon of coconut aminos mixed with a dash of vinegar, as traditional Worcestershire can be high in sugar.
Use high-quality, full-fat cheese for the best melt and flavor.
This soup freezes well if you omit the heavy cream until reheating. Add the cream after thawing and reheating.