Saute the minced garlic and butter in a large nonstick skillet over low heat. Stir frequently, do not let the garlic brown.
Remove from heat. Pour into a blender, and keep skillet out for the chicken and broccoli
In a large pot, bring water and vegetable broth to a boil, add cauliflower, and cook until cauliflower is fork tender, about 6-8 minutes. Don't drain, you need that liquid!
While the cauliflower is cooking, prepare your noodles according to package directions.
Put frozen chicken strips, and broccoli in the skillet, add 1/2 a cup of liquid from the cauliflower cooking pot if needed. Turn on medium heat, and warm chicken through. The broccoli should get softer, but stay crisp while the chicken heats.
Spoon cauliflower out of pot and into the blender with the butter and garlic, add in about a cup of the cooking liquid, salt, pepper, and milk.
Blend until smooth.
Add in the olive oil, and cheeses, and blend again. You want to puree until the sauce is very smooth. If your blender is small, do this in batches. Taste and adjust to your preference, adding more cheese or seasonings.
Add noodles to pan with broccoli and chicken, toss, and pour alfredo over the top!