Melt butter in a large pot over medium heat. Saute onion until translucent, about 5 minutes.

Whisk in the flour cooking until the color becomes golden, adding 1 to 2 tablespoons of heavy cream if necessary to keep the flour from burning, about 3 to 4 minutes.

Slowly pour the heavy cream into flour mixture while whisking constantly. Stir chicken stock into the heavy cream mixture. Bring this to a simmer;continuing to cook until the mixture has thickened, about 20 minutes.

Add carrots; simmer until they are tender, about 10 minutes. Add the frozen broccoli and continue to cook for an additional 10 minutes.

Stir Cheddar cheese into vegetable mixture until cheese melts.

Season with salt and pepper to taste.

Bread bowls:

Using a sharp knife, cut a circle into the top of each loaf, leaving a 1-inch border all around. Remove the bread top, then hollow out the middle with a fork or your fingers, leaving a thick bread shell.

Scoop soup into each bread bowl. Serve as is or top with additional grated cheese.