Fumbling Toward Culinary Talent: Broccoli Cheese Soup

This is a variation on the cheese soup recipe I saw on the aforementioned episode of Good Eats. 

Ingredients
Half of a yellow onion, finely chopped
1 large carrot, finely chopped
1 large stalk of celery, finely chopped
2 tablespoons of unsalted butter
3 tablespoons of all-purpose flour
32 oz. of chicken stock
1 minced clove of garlic
1 cup of heavy cream
1 bay leaf
7 ounces of gouda, shredded
3 ounces of smoked gouda, shredded
1 package of steamed broccoli
Smidge of tyme
Salt and pepper to taste

Process
Heat a dutch oven to medium and melt the butter. Sweat the onion, carrot, and celery until soft. Coat the mixture with flour and cook for approximately a minute. Add the stock, bring to boil, and then move it back to a simmer. 

Add the garlic and bay leaf. Simmer for 10 minutes.Use a handheld mixer to blend the aromatics. 

Add the heavy cream and continue over a slow simmer. Add the shredded cheese in bunches. In the meantime, steam the broccoli and add into the soup. Simmer for five minutes.