In a large pot, heat butter on medium and sauté shallot until soft. Add mushrooms and cook until water releases (about 5 min). Stir in flour and cook 1-2 minutes longer. Stir in broth and milk. Continue stirring until mixture thickens. Add salt and pepper to taste. Use in casseroles or thin with milk for a soup. Store in air tight container in refrigerator for up to a week or freeze for later use.