Melt the butter in a large pot over medium heat.
Add the garlic and onion and cook for 2-3 minutes until fragrant.
Stir in the carrots and flour and cook for 1 minute.
Pour in the broth and heavy cream and bring to a simmer.
Add the broccoli, salt, pepper, paprika, onion powder, and cayenne.
Simmer for 10-15 minutes until the broccoli is tender.
Remove from heat and stir in the shredded cheddar cheese until melted and smooth.
