Preheat oven to 375 degrees F.
In the bowl of a stand mixer, using the whisk attachment, beat the cool butter and shortening until creamy. Add the egg and vanilla and continue to beat until creamy. It may look a bit curdled at first. Keep beating for about 2 minutes.
In a second bowl, whisk together the sugars, baking powder, baking soda, salt and flour until evenly mixed.
Add flour mixture to the egg and butter mixture. Return mixer to mixer stand. Using the paddle, beat on medium until evenly blended but still rather crumbly. Empty onto a pastry mat and knead gently until dough comes together. Knead in the chocolate chips and nuts. If using gluten-free dough, you should be able to just stir in the chips and nuts, but the all-purpose dough is a little dryer.
Shape dough into balls that are about 1 inch in diameter or about 30 to 32 grams each.
Arrange the dough balls about 1 ½ to 2 inches apart and bake one sheet at a time (or you can do two sheets if you prefer) for about 12 minutes or until cookies appear golden and cracked. Update -- Bake longer if the cookies do not appear lightly browned around the edges. They will be slightly soft when you pull them from the oven and need time to cool and crisp.
Let cool on the baking sheet for about 3 minutes, then carefully transfer to a wire rack to cool and crisp.