Heat the oil in a pot over medium heat. Sauté the onions and garlic until golden brown. Stir in the flour and cook for 1-2 minutes.
Stir the broth and broccoli. Season with salt and pepper. Cover with a lid and bring to a simmer for about 15 - 20 minutes until the flavor builds. Stirring occasionally.
Stir the cream and cheese into the soup until it melts completely. Taste and adjust the seasoning with salt if needed.