Heat the olive oil in a large pot over medium heat. Add the onions and garlic and cook for 5-6 minutes until softened. Stir in the flour.
Whisking constantly, gradually pour in the milk. Add the chicken broth and broccoli florets. Bring to a boil, then reduce to a simmer and cook for 8-10 minutes until the broccoli is tender.
Stir in the cheddar cheese, followed by the heavy cream. Taste and add salt and pepper to taste. Enjoy!
