Prepare the Vegetables

1. Chop the Broccoli: Begin by cutting your broccoli into bite-sized florets. If you’re using frozen broccoli, just thaw and set it aside.
2. Chop the Onion and Garlic: Finely chop your onion and garlic. This will allow them to infuse the soup with their savory flavor.

Cook the Vegetables

1. Sauté the Onion and Garlic: In a large soup pot, melt the butter over medium heat. Add the chopped onion and sauté for about 5 minutes, until it becomes soft and translucent. Add the garlic and cook for another 1-2 minutes, until fragrant.
2. Add the Broccoli and Seasonings: Toss the broccoli florets into the pot, stirring to coat them in the buttery onion and garlic mixture. Sprinkle in the salt, pepper, and thyme. Stir to combine, letting the vegetables cook for another 2 minutes.

Simmer the Soup

1. Add the Broth and Milk: Pour in the vegetable (or chicken) broth and bring to a simmer. Allow the soup to simmer for about 10-15 minutes, or until the broccoli is tender but still slightly crisp.
2. Thicken the Soup: While the soup is simmering, make a simple roux to help thicken the soup. In a small saucepan, melt the remaining butter. Add the flour and whisk for 1-2 minutes until golden and bubbling. Slowly pour in a bit of the hot broth from the soup, whisking constantly, until smooth. Then, pour this thickened mixture into the soup pot, stirring to combine. Continue to simmer for another 5-10 minutes, until the soup thickens to your desired consistency.

Add the Cheese

1. Melt the Cheddar: Turn the heat to low and gradually stir in the shredded cheddar cheese, a little at a time, until the cheese is fully melted and the soup is creamy and smooth. Taste the soup and adjust the seasoning if needed, adding more salt, pepper, or a pinch of nutmeg for depth.

Serve and Enjoy

1. Serve: Ladle the soup into bowls, topping each with a sprinkle of extra shredded cheddar cheese or a pinch of fresh herbs if desired. Serve immediately with a side of crusty bread or a light salad for a complete meal.