Beat butter and sugar at medium speed with an electric mixer until fluffy. Add egg and vanilla, beating well. Add flour, beating just until mixture is blended.
Divide dough into 3 portions; roll each portion on wax paper into a 12-inch log. Cover and chill 8 hours.
Cut each log into 1/2-inch-thick slices; place on lightly greased baking sheets. Press thumb in center of each slice to make an indentation; fill with 1/2 teaspoon preserves.
Bake at 350° for 10 minutes or until edges are lightly browned. Remove to wire racks to cool. Freeze, if desired.
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