In a large Dutch oven on medium heat, saute the diced onion in ¼ cup of butter until soft and lightly browned.
Add the chopped broccoli and carrots and stir with the carrots until the broccoli and carrots natural colors are bright. About 2-5 minutes. Add the buttermilk and broth.
Next, pour the ¼ cup of reserved chicken broth into a small bowl with the ⅓ cup of cornstarch. Use a fork to dissolve the cornstarch into the broth and turn it into a slurry.
Pour the cornstarch slurry into the Dutch oven, stir all of the ingredients, and bring to a simmer. Season with salt and pepper to taste and add the garlic powder. Let simmer for 20-25 minutes.
Reduce the heat to low or take the Dutch oven off the burner and pour in the 3 cups of cheddar cheese. Mix thoroughly until the cheese is melted and incorporated. If your soup is too hot, the cheese will have a grainy texture, so make sure the soup is not too hot.
Return the Dutch oven to a low simmer so the soup is hot. If you want the soup to be thinner, you can add extra stock or buttermilk to get the soup to the thickness you prefer. If you would like the soup to be thicker, you can take a ¼ cup of broth, water, or buttermilk and blend it with 1 tbsp of cornstarch to create another slurry and mix that into the soup.
Serve the soup hot. If you want to keep the whole meal gluten-free, serve with a salad or roasted meat and vegetables. You can also serve the gluten-free broccoli cheddar soup with sourdough bread even though sourdough is not gluten-free.