Place broccoli in microwave safe dish, and cook according to package instructions. Microwave broccoli until fork tender.
Heat a large saucepan over medium heat, then add olive oil. Add onion and garlic and saute until translucent and aromatic, 3-5 minutes. Add flour to pan and quickly stir until flour is cooked and incorporated; add broth, ¼ cup water and half of the broccoli florets.
Transfer mixture to a food processor and blend about 10-15 seconds. Return mixture to pan and bring to a boil. Cook for 3-5 minutes, to let mixture thicken.
Decrease heat and add the rest of the broccoli, half and half and shredded cheese. Stir until cheese melts; let soup cook a little longer. Season with salt and pepper. Add crushed red pepper flakes, if desired. Top soup with shredded cheese of choice.
Recipe by sweet caroline's cooking at https://sweetcarolinescooking.com/2013/01/09/back-on-track-quick-broccoli-cheese-soup/