In a dutch oven or large soup pot, melt the butter over medium-high heat.
Saute the onion and garlic in the butter for 2-3 minutes.
Add the flour and quickly whisk.
Pour in one cup of the chicken stock, and whisk until the mixture is smooth.
Add the remaining 2 cups of chicken stock and whisk again.
Add in the milk, heavy cream, dijon mustard, pepper and hot sauce. Whisk constantly over medium heat for about 3-5 minutes until the mixture starts to steam and almost comes to a boil. Then turn the stovetop medium-low heat.
Add in the broccoli and shredded carrots. Cook, stirring often, for about 15-20 minutes until the broccoli is tender. The exact timing will depend on the size of the broccoli florets.
If you'd like a smoother soup, use an immersion blender to purée about one third to half of the soup. Or you can leave the soup with the larger vegetable pieces.
Once the broccoli is tender, turn the heat to low and add in the shredded cheddar cheese, about ¼ cup at a time, stirring so that the cheese melts between each addition.
Serve immediately.
Notes
The soup will continue to thicken as it sits. If it gets too thick, add a little more milk to thin.Refer to the article above for more tips and tricks.The calories shown are based on the recipe making 8 servings, with 1 serving being 1/8 of the soup. Since different brands of ingredients have different nutritional information, the calories shown are just an estimate. **We are not dietitians and recommend you seek a nutritionist for exact nutritional information. The information in the nutrition box are calculated through a program and there is room for error. If you need an accurate count, I recommend running the ingredients through your favorite nutrition calculator.**