Add 1 Tbsp butter dutch oven & warmth within MED heat. Add chopped onion & saute until onions are tender & translucent, about 2-3seconds. Insert ¼ cup butter oven, nevertheless over MED warmth. When meltedadd flour & whisk together. Cook mix around a minute, whisking frequently.
Gradually pour about a cup of chicken-broth, whisking as you pour. Proceed with remaining chicken broth & half and half, massaging gradually & invisibly as your pour.
Permit broth/half & half mix cook for a moment or 2, whisking frequently, which makes certain that no flour lumps stay.
Add carrots & broccoli & stir to blend. Add paprika, garlic powder, dry mustard, pepper & salt, stir fry. Reduce heat to LOW/MED LOW & simmer approximately 10-15mins or till thickened & broccoli/carrots are tender. If soup becomes too thick for your liking, add a dash of chicken broth or half & half an hour to loosen this up.
Blend soup until desired texture is attained, utilizing either immersion blender or from shifting soup to classic blender.
Add grated cheddar-cheese a few at a time, stirring to melt-cheese to the soup after every handful. Taste soup & season with salt & pepper if necessary.
Serve hot with extra black-pepper & toasted cheese on top if needed.