Gather the ingredients.
Sift the flour, baking powder, baking soda, and salt into a medium bowl.
In a large bowl, use an electric mixer to beat the butter, shortening, and white and brown sugars.
Add the eggs and almond extract, and beat until well blended.
Stir in the flour mixture and mix well. The dough will be dry and crumbly at this point.
Use your fingers to form the mixture into a dough, and then form the dough into 2 rolls or logs that are 10 to 12 inches long. Wrap and refrigerate for at least 2 and preferably 4 hours. (If desired, you can prepare the dough ahead of time and refrigerate overnight).
Preheat the oven to 325 F.
Take a log and lightly score the dough at 3/4 inch intervals so that you have 15 pieces and cut the dough.
Roll each piece into a small ball and roll the ball in the bowl of sesame seeds to cover. (Note: If you like you can brush the ball with lightly beaten egg prior to dipping in the sesame seeds, to help the seeds stick to the cookie).
Place the balls on a lightly greased cookie tray, approximately 2 inches apart.
Bake the cookies at 325 degrees for about 15 to 17 minutes, or until a fork inserted in the middle comes out clean and they easily lift from the baking sheet. Cool completely.
When thoroughly cooled, enjoy or store in a sealed container.