Wash broccoli and trim off florets.

In a large pot, melt butter and cook onions over medium-low heat. Onions should be softened, but not browned.

Add broccoli florets to pan and saute until bright green, about 4 minutes.

Add chicken broth to pot and increase heat to medium high.

Simmer just until broccoli is tender, about 7 minutes.

Use immersion blender, or regular blender to puree soup until smooth.

In a regular blender, puree in two batch and take care to vent blender while pureeing to avoid burns.

Return blended soup to pot and stir in half and half.

Add cheeses and stir until melted.

Season with salt and pepper.