Heat A Large Pot Over High Heat.
When Hot, Add Butter, Garlic, Onions, Carrots, Mushrooms, And Celery.
Sauté Until Vegetables Soften, About 3–4 Minutes.
Add Flour And Stir.
Reduce Heat To Medium-High And Cook For 1 Minute Before Adding Broth.
Continue To Stir And Allow The Mixture To Come To A Boil And Thicken, About 5 Minutes.
Add Half And Half And Cheddar.
Stir And Allow Cheddar To Melt And Combine With Broth Before Adding Broccoli, Cauliflower, Salt, And Pepper, About 2 Minutes.
Bring To A Gentle Boil, Reduce Heat, And Simmer For 5 Minutes Before