Melt butter in a heavy 12-inch skillet over medium-high heat. Add mushrooms and shallot. Saute, stirring occasionally, until softened, about 6 minutes. Add 2 tablespoons plus 2 teaspoons flour; cook until incorporated, about 1 minute. Add beef broth; cook, stirring frequently, until slightly thickened, about 2 minutes. Stir in half-and-half, black pepper, and salt. Cook for 30 seconds more.