In a large saucepan, cook butter, onion and carrots over medium heat until onion softens (about 3 minutes). Add chicken broth, broccoli and seasonings. Simmer until broccoli is softened, about 8 minutes.
Remove 1 cup of vegetables, coarsely chop and set aside. Using an immersion blender, blend remaining vegetables and broth.
Place flour in a small bowl. Add in cream a little at a time stirring until smooth. Bring blended vegetable mixture to a boil and whisk in cream mixture. Continue whisking until thick and bubbly, about 3-4 minutes.
Remove from heat, stir in cheeses & reserved chopped vegetables and serve immediately.