Melt the butter in a large pot on medium heat.
Stir in the onions & garlic. Cook for 5-7 minutes.
Add the flour and mix well, until the flour is fully incorporated, creating a roux.
Whisk in the vegetable broth and rice milk until roux is completely incorporated. Bring mixture to a boil.
Bring soup back to medium heat and add broccoli & carrots. Cook for 10 minutes.
Add cheddar cheese (we love Follow Your Heart) and stir until cheese is completely melted.
Remove about 1/4 of the soup from the pot and place it in a high speed blender. Blend until creamy. Add back to the pot and stir well.
Add salt and pepper to taste and enjoy! We love to add croutons or bread to the soup when serving.