In a mixer or large bowl, cream together butter, solid coconut oil, and sugar until well combined. Add the egg yolk (save the egg white for the egg wash) and mix until well combined. Add the flour, baking powder, lime juice, and lime zest to the same bowl and mix until a dough forms.
Transfer dough to a work surface and shape into a smooth log. You may need to flour your hands so it's easier. Wrap the log in plastic wrap and chill for at least 2 hours or overnight. Don’t skip this step!
Preheat oven to 350 degrees Line a baking sheet with parchment paper. Set aside.
Remove logs from the fridge. Slice log into 12 evenly thick cookies and place on the baking sheet. Brush the cookies with whisked egg white (egg wasand sprinkle with sugar.
Bake the cookies for 15-20 minutes or until brown around the edges. Allow to cool completely before serving. Enjoy!