In a large bowl, sift together the cake flour, baking powder and salt. Use a sifter, so you have light fluffy flour that wont clump.
In a separate medium sized bowl or the bowl of a stand mixer, beat together the butter, shortening and sugar. Mixture should be very pale yellow and fluffy.
Vigorously beat in the egg, egg white, vanilla extract and almond extract using a wooden spoon or a paddle attachment of a stand mixer.
With the stand mixer on low, beat in the flour mixture about 1/2 at a time.
Cover the bowl with plastic wrap and refrigerate for at least 3 hours or overnight.
After completely chilling the cookie dough, preheat the oven to 350F degrees.
Prep cookie sheets by lining with parchment paper, nonstick foil, or silicone baking mats. I prefer parchment paper.
Roll the dough into ping pong sized balls and place 2 inches apart on a baking sheet.
I try to flatten the dough in my hands, to make a thin disc shape, or will use a silicone rolling pin or even the bottom of a cup. Just toss a little flour on your hands or whatever you're using so it doesn't stick!
Bake for 9-11 minutes, or until the tops are set.
Do not over cook, as these cookies are best when not browned around the edges like a chocolate chip cookie.