Preheat oven to 350 degrees. In a large bowl, using an electric mixer, beat butter and sugar until smooth. Add egg, and beat until completely combined. With mixer on low, add flour, and mix just until incorporated.
Shape dough into 1-inch balls (about 2 tablespoons each). Place on baking sheets, at least 3 inches apart.
Moisten thumb with water, and gently press the center of each ball, making an indentation about 1/2 inch wide and inch deep. Spoon about 1/2 teaspoon into each indentation. Bake until cookies are golden brown around edges, 18 to 20 minutes. Transfer to a wire rack, and let cool completely. If storing, place in an airtight container at room temperature, up to 2 days or freeze for longer storage.