1 tablespoon butter (for sautéing)

1/4 cup unsalted butter

1 small yellow onion, finely chopped

1/4 cup all-purpose flour

2 cups chicken broth (or vegetable broth for vegetarian)

2 cups half and half (or whole milk)

3 cups fresh broccoli, roughly chopped

1 cup carrots, peeled and chopped

1/2 teaspoon kosher salt

1/4 teaspoon paprika

1/4 teaspoon garlic powder

1/2 teaspoon dry mustard (or 1/2 tsp regular mustard)

1/4 teaspoon black pepper

2 cups shredded sharp cheddar cheese