Preheat oven to 350ºF.
In a large mixing bowl with an electric mixer, blend together coconut oil, light butter and peanut butter for about 1 minute, until very smooth and combined.
Add the sugars and beat for 1-2 minutes, until light in color and combined.
Gradually beat in the egg and vanilla, just until blended.
Mix in the flour and baking powder until combined together.
Scoop up a tablespoon of dough and roll into a ball. Roll in sugar and place on a nonstick baking sheet (or cover a baking sheet with parchment paper).
Using the tines of a fork, flatten each cookie in a cross pattern (as shown in the pictures).
Bake for 15 minutes, or until golden brown. Remove to a rack, cool and then enjoy!