In a large bowl, cream the butter. Add the brown sugar and granulated sugar, and beat until light and fluffy. Beat in the egg and then the vanilla.
Sift or stir together the flour, baking soda, and cream of tartar. Gradually add the dry ingredients to the creamed mixture, stirring just until blended. Divide the dough in half, wrap it in waxed paper, and chill it for at least 3 hours.
Working with 1 portion at a time, roll the dough out to the thickness of 1/4 inch (5mm) or less. With a 2 1/2 inch (7 cm) round cutter, cut out the cookies. With a very small round cutter, cut a hole out of the centre of half of the cookies. With a metal spatula, transfer the rounds to ungreased baking sheets, spacing them about 1 1/2 inches (4 cm) apart.
Bake the cookies in a 375°F oven for about 8 minutes, or until lightly browned. Let the cookies cool on wire racks.
Sprinkle icing sugar on the cookies with the holes. Spread the whole cookies with jam and top each with a sugared cookies.