Melt butter in a large skillet over medium heat. Add shallot and garlic; cook, stirring, until softened, about 3 minutes. Add mushrooms and 1/4 teaspoon salt; cook, stirring, until mushrooms have softened and released their liquid, about 7 minutes. Raise heat to medium-high; cook until liquid has evaporated, about 3 minutes more. Stir in parsley, 1/2 teaspoon salt, and the pepper. Let cool completely.