Heat a large Dutch oven over medium-low heat. Add butter and oil and heat until butter foams.
1 tablespoon unsalted butter, 1 tablespoon olive oil
Add onion, carrots, and fennel. Cook for 4 minutes or until slightly softened. Keep stirring occasionally.
1 medium yellow onion, 2 medium carrots, ½ small fennel
Add garlic and cook for another 30 seconds. Stirring often.
2 medium cloves garlic
Sprinkle flour over the vegetables and stir. Cook, stirring often, until mixture begins to brown on the bottom of the Dutch oven.
3 tablespoons all-purpose flour
Gradually pour in the chicken broth while deglazing the bottom of the pan.
2½ cups unsalted chicken broth
Add the blanched broccoli and stir.
Whisk in the wine and half-and-half, mixing until well incorporated.
¼ cup medium-dry white wine, 2½ cups half-and-half
Add the red pepper flakes and bay leaf.
1/8 teaspoon crushed red pepper flakes, 1 bay leaf
Increase the heat to medium and bring the soup just to a boil, stirring often. Reduce the heat to low and simmer 10 minutes or until vegetables soften. After the vegetables have softened, add the cooked gnocchi, stir gently.
Remove the soup from the heat and discard bay leaf. Add the cheese and stir until the cheese melts.
12 ounces shredded sharp cheddar cheese
Taste the soup and, if necessary, season with kosher salt and freshly ground black pepper. Serve immediately with baguette slices.
Kosher salt and freshly ground black pepper