Melt the butter in a large pot over medium-high heat. Add in the onions, carrots and broccoli florets. Cook to soften for about 5 minutes.
In a small bowl mix ½ cup of milk with the ¼ cup of flour.
Slowly add in the broth, the remaining ½ cup of milk and cream. Stir in the prepared milk and flour mixture. Add salt, black pepper, and crushed red pepper flakes. Continue stirring and heat over medium heat until thickened, about 10-15 minutes.
Once the soup has thickened, stir in the cheddar cheese until melted and smooth.