In a large pot or Dutch oven, melt butter over medium heat. Add onion and cook until softened, about 5 minutes. Add garlic and cook for 1 minute more.

Stir in flour and cook for 1 minute, creating a roux.

Gradually whisk in chicken broth until smooth. Bring to a simmer.

Add broccoli florets and cook until tender, about 10-15 minutes.

Stir in heavy cream and cheddar cheese until cheese is melted and smooth.

Season with salt and pepper to taste.

Serve immediately.