Preheat the oven to 350°F. Lightly grease the baking sheets. In a medium bowl, whisk together the flour, baking powder, and salt; set aside. In a large bowl, with an electric mixer on medium speed, cream the butter and sugar together until pale in color. Mix in the egg. On low speed, add about half of the flour mixture. Add the cream and vanilla extract. Slowly add the remaining flour and mix the dough until thoroughly blended.

Divide the dough in half and shape each half into a flattened ball. Wrap the dough tightly in plastic wrap and chill for 30 minutes or until firm enough to handle. It may be chilled overnight.

On a lightly floured surface, using a lightly floured rolling pin, roll half of the dough 1/4 inch thick. Lift the dough occasionally to check if it is sticking. Lightly reflour the work surface and rolling pin as needed. Cut out the cookies with a 2-1/2-inch cutter and place them 1 inch apart on the baking sheets. Reroll the scraps and cut out cookies. Repeat with the second half of dough.

Bake in the center of the oven for about 10 to 12 minutes, or until just set but not brown around the edges. Let the cookies cool on the baking sheet for a few minutes, then transfer them to a wire rack to cool completely.

Prepare the vanilla glaze: Use a pastry brush or small spatula to frost the cookies while they are still warm (this causes a nice sheen). Let the cookies dry thoroughly. Store in an airtight container between sheets of waxed paper to prevent icing smudges. Well-wrapped cookies may be frozen.