Easy and fast way to steam broccoli is in the microwave. Dice broccoli and spread it in one even layer on a large plate. Add about a tablespoon of water to the plate. (If you have a microwave steam bowl with a lid, that’s perfect.) I use a microwave plate cover but if you don’t have one, you can use another deep plate turned upside down to cover with just leave a little crack for steam.
Microwave for about a minute and a half and set aside.
No microwave? No problem. You can steam broccoli in a steamer on the stove-top. It will take a little longer but it's a good option.
Note: if you got a broccoli bunch, you can dice some of the broccoli stems and sauté it with onions and carrots for more broccoli flavor.
Make the Soup:
Preheat the Dutch oven over medium heat and add butter. Let butter melt and add diced onion and carrots (and diced broccoli stems if using). Let it cook, stirring once in a while, until softens and starts to get golden-brown.
Add minced garlic, stir and sauté until garlic is fragrant.
Sprinkle flour over the veggies and stir to mix. Pour in the chicken stock as you slowly stir the veggies and then pour in the milk and add seasoning.
Heat the creamy broth through first, then lower the heat to medium-low. Then, start adding grated cheddar cheese one handful at a time as you stir slowly.
Add steamed broccoli and heavy whipping cream. Stir and let it cook for a few minutes. Take off heat.