Use an electric mixer to cream together butter, sugar and peanut butter.

Add egg and beat until well blended.

In a bowl, combine flour, salt and baking powder.

Add dry ingredients to the wet ingredients, adding a little milk as necessary to make dough just soft enough to handle.

Stir in the vanilla.

Shape dough into a log about 1 ½ inches in diameter; wrap in plastic and refrigerate for at least 2 hours or up to 2 days (or wrap well and freeze).

Heat oven to 400 F.

Lightly grease 1 or 2 baking sheets.

Cut slices about ⅛-inch thick from chilled or frozen log.

Bake until edges are lightly brown and center is set, 6-10 minutes.

Cool for about 2 minutes on sheets before using a spatula to transfer cookies to a rack to finish cooling.

Sandwich flat sides of two cookies together with a heaping teaspoonful of jam; repeat using all cookies.