Preheat the oven to 350F (180C) and line two large cookie sheets with parchment paper.
In a large mixing bowl, beat the butter and sugar until light and fluffy. About 3-4 minutes.
Add the egg and vanilla paste and mix to incorporate fully.
In a medium bowl, sift the flour, cornstarch, and baking powder.
Gradually add the flour mixture to the butter mixture until you have a smooth dough.
Divide the dough into two parts, and roll each to 1/4-1/2 inch thickness over a floured surface. (flour your rolling pin as well).
Cut the dough using a 2-3 inch cookie cutter, and place the cut dough over the prepared cookie pans.
Use a 1/2-inch round cookie cutter or the back of a piping tip to cut half of the cookies at the center.
Bake for 12-18 minutes (less time for small/thinner cookies and more time for larger/thicker cookies) until the sides are slightly golden.
Remove from the oven and allow to cool completely.
Dust the cookies with the whole in them with powdered sugar and top the rest with 1/2-1 teaspoon of strawberry jam.
Top with the powdered cookies and serve.