In a saucepan, melt 2 tablespoons of butter over medium heat.
Stir in the flour and cook for about 1 minute, until bubbly.
Gradually whisk in the chicken broth and milk, and bring the mixture to a boil. Cook, stirring, until the sauce thickens.
Remove from heat and stir in the sour cream, Dijon mustard, and half of the cheddar cheese. Season with salt and pepper to taste.