In a Dutch oven or large pot, melt the butter over medium-high heat. Add the onion and cook until translucent, about 3 minutes.
Add the garlic and cook until fragrant, about 1 minute. Then add the flour, stirring frequently, and cook the flour for about 2 minutes.
Add the vegetable stock, crushed red pepper flakes, nutmeg, paprika, salt, and pepper. Then add the broccoli. Bring to a boil and then lower the heat to medium-low. Simmer for 10-15 minutes until the broccoli is tender-crisp and the stock has slightly thickened.
After the stock has slightly thickened, this next step is optional. I like to take my immersion blender and blend up some of the soup to smooth it out. I still like chunks of broccoli, so I don’t completely smooth it out. How smooth you like it is up to you!
Now add the heavy cream and shredded carrots. Cook for about 5 minutes until the carrots have softened.
Add the shredded cheddar, stirring frequently until it has melted. The longer this soup cooks, the more that it will thicken. If you need it thicker faster, add a littler cornstarch (mixed with a little water) and cook until thickened to your preference.
Serve the soup with a little extra shredded cheddar on top with some fresh bread on the side. Enjoy!!
Store leftover soup in the refrigerator for up to 5 days. Reheat in the microwave until warm. You may need to add a little more vegetable stock or milk to loosen the soup up.