Broccoli Cheese Soup

Pretty great broccoli cheese soup. Goes well with a roast beef sandwich.

===== Ingredients =====
-5tbsp unsalted butter
-1 small onion, finely diced
-1 clove garlic, minced
-1/4c AP flour
-2c chicken or vegetable stock
-2c half and half
-2 to 3c broccoli florets
-2 large carrots, cut into thin rounds
-salt
-pepper
-paprika
-cayenne
-8oz shredded cheddar

===== Instructions =====
1. Saute onions in pan with 1tbsp butter until translucent. Add in onion and cook for a few seconds more. Set aside.
2. In a medium saucepan, melt remaining butter. Add in flour and cook 3-5 minutes, until roux has thickened.
3. Add in stock and half and half. Whisk together, allow to simmer for 10-15 minutes.
4. After simmering, add in broccoli, carrots, onions/garlic mixture. Season to taste with salt, pepper, paprika, and cayenne.
5. Simmer for 20 minutes.
6. Mix in cheddar, stirring well until all the cheese has melted. Serve.