In a large saucepan or pot, cook butter, onion, and carrots over medium heat until onion softens (about 3 minutes). Add the broccoli, chicken broth, thyme, garlic powder, salt, and pepper. Simmer until broccoli is tender, 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.
