Melt the butter in a large Dutch oven or stockpot over medium-high heat. Add the onion and carrots, and cook until the onions are translucent (approximately 5 minutes). Add the garlic and cook for an additional 30-60 seconds. Add the flour and stir to coat. Continue cooking for approximately 3 minutes, stirring periodically, to cook out the flour taste.
Stir in 1 teaspoon of salt, the stock and half-and-half. Bring to a simmer and cook until the soup has thickened, about 10 minutes. Add the broccoli and simmer until crisp-tender, about 5 minutes. Remove from the heat.
Add 1 teaspoon of pepper and sprinkle in cheese by the handful, stirring. Allow the cheese to melt before adding more. (Note: it’s important to do this off the burner, since too much heat can cause cheese to separate and become gritty). Taste for seasoning and add the remaining salt and pepper if desired.
Broccoli is one of my favorite vegetables, so the one change I made to the original recipe was to double the amount of broccoli used, totaling 4 cups.Freshly grated cheese will definitely offer the best flavor. However, 4 cups takes a long time to grate by hand. I highly recommend using the grater attachment on a food processor, if you have one.Reheat this soup low and slow on the stovetop, stirring frequently. If you heat it too quickly, the cheese might separate.Shared with permission from The Simple Kitchen, by Chad and Donna Elick.