Melt the butter and the shortening mixture together. Combine the shortening mixture with 1 1/2 cups sugar in a mixing bowl and mix well. Add the 3 eggs and continue mixing until creamy. Add the brandy, almond extract, butter flavoring, and the baking powder. Mix well. Slowly begin adding the flour, and beat until the mixture leaves the side of the bowl. Set aside.
Spray the cookie sheets with cooking spray and then wipe them off.
Using a small ice-cream scoop, begin cutting the balls out of the dough. Press a ball of cookie dough down, using a clear plastic lid from the baking powder can, so they will all be the same size.
Pick up 1 cookie at a time, and brush with the egg white mixture, and press into the topping mixture. Press the cookie down, pick it up to shape it in your hand, and press your finger in the middle to make a dent.
Bake in the oven for 20 to 25 minutes until golden. When serving, put a 1/2 teaspoon of the apricot preserve in the middle of the cookie.