Saute the aromatics. Add the butter to a large, heavy-bottomed pot and melt. Add in the onion and sauté over medium heat until translucent. Add the garlic and cook a minute more, just until fragrant.
Build the roux. Add the remaining butter and melt, then sprinkle in the flour. Allow the flour and butter to make a roux, and whisk as it cooks for a few minutes – make sure to allow it to thicken into a sort of paste, or the soup will not thicken correctly later.
Make it soup! Stir in the stock, milk, and cream and simmer over medium-low for 15 minutes. Add in your seasonings and vegetables and continue to simmer over medium heat for about 15 minutes, or until the broccoli is tender to your liking.
Finish the Broccoli Cheddar Soup. Turn off the heat. Stir in the shredded cheese and allow to melt. Serve immediately. It’ll store in an airtight container in the fridge for about 3-4 days.
