Place a medium Dutch oven or stockpot on medium-high heat and melt the two tablespoons of butter.
Add the minced garlic to infuse in the butter and after a minute add in the chopped broccoli and stir. Cook for 2-3 minutes and pour in half the chicken bone broth.
Put the rest of the chicken bone broth in a high-speed blender then add in the cream cheese, chopped cauliflower, onion powder, mustard powder, and egg. Blend on high for 30-45 seconds until the mixture, especially the cauliflower, is completely smooth.
Pour the mixture into the Dutch oven with the broccoli and bone broth. Heat to boiling then turn down the heat to a simmer for at least 10 minutes, stirring occasionally.
Whisk in the cheddar cheese until it's melted and dispersed throughout. Add black pepper and salt to taste and serve immediately or continue to simmer to blend the flavors.