01 -
Grate the cheese and put it aside. Get all other ingredients measured and ready to make cooking easier.
02 -
Heat up the butter in a big soup pot on medium. Toss in the chopped onions and let them get soft for about 5 minutes, stirring now and then.
03 -
Toss in the garlic, Worcestershire sauce, hot sauce, and all seasonings, cooking for a minute more. Sprinkle the flour in and stir for 1-2 minutes to get rid of that raw flour taste.
04 -
Slowly pour in the chicken stock a bit at a time, always stirring to keep things smooth. Do the same with the half and half. Let everything bubble gently and thicken for about 5-7 minutes. Keep stirring and use your spatula to stop any sticking.
05 -
Dump in the broccoli and carrots, partly cover the pot, and cook until they're soft, about 10 minutes. Stir once in a while and keep the heat low enough for just tiny bubbles.
06 -
When you can easily stick a fork in the broccoli, turn the heat down low. If you want it smoother, use a hand blender on some of the soup, then stir it all back together.
07 -
Slowly add your cheese while the heat's on low, stirring until it's all melty and mixed in. Serve it hot right away!