Place the broccoli with ½ cup of water in a glass bowl covered in saran wrap in the microwave for 3-4 minutes while you prepare the rest of the soup.
Simmer vegetable broth and chopped onion for 5 minutes in large saucepan, until onions are soft. Add milk and lightly sprinkle the flour, mixing it at the same time.
Cook, stirring constantly until soup starts to thicken, about 5-8 minutes.
Add cheeses and stir until completely melted. Stir in cooked broccoli florets.