Lightly spoon flour into a dry measuring cup; level with a knife. Place peanut butter, sugar, and egg in a medium bowl; beat with a mixer at medium speed until smooth. Add flour; stir well. Shape dough into 36 (1-inch) balls; place 1-inch apart on baking sheets coated with cooking spray. Press thumb into center of each cookie, leaving an indentation. Cover and chill 3 hours.
Preheat oven to 375°.
Bake cookies at 375° for 12 minutes or until golden. Remove from pans; cool on wire racks. Spoon 1/2 teaspoon jam into the center of each cookie.