Heat oven to 350°F. Beat butter, flour, sugar and egg in medium bowl with electric mixer on medium speed until smooth. Beat in ginger just until combined.
Shape dough into 1-inch balls. Place about 1-inch apart on ungreased cookie sheet. Make indentation in each ball with finger or handle of wooden spoon.
Bake 12 to 15 minutes or until edges just begin to brown. Remove from cookie sheet to wire rack. Cool completely, 15 to 20 minutes.
Fill indentation in each cookie with slightly less than 1/4 teaspoon of the jam.