Melt 1 Tbsp of butter over medium heat, saute the onion and set aside. Add 1/4 cup butter,
melt, then add 1/4 cup of flour and whisk together over medium heat for about 3-4 minutes.
Slowly whisk in the half and half and chicken stock. Let it simmer for about 20 minutes. If you
don't have half and half or wanted to try regular milk, I think that would probably work too.
Add the broccoli, carrots, and sauteed onions. Let them simmer on medium low for about 25
minutes until the broccoli and carrots are tender.
Add paprika, garlic powder ground dry mustard, salt and pepper and sharp cheddar cheese.
Stir until cheese is melted.
If you like a smoother soup, transfer to food processor or blender and blend until smooth.