Preheat oven to 350°F. In a large bowl, whisk to combine tapioca and coconut flours, baking powder, xanthan gum and Himalayan salt. In a large bowl of an electric mixer fitted with the paddle attachment, cream together butter, coconut oil and coconut sugar until very light and fluffy, about 2 minutes. Beat in egg and vanilla until combined, then flour mixture.
Divide dough into two portions. Between two pieces of parchment, roll one dough portion to the thickness of 1/4-inch. Use cookie cutters to cut cookies into shapes and transfer to parchment-lined baking sheets. Repeat with remaining dough and any scraps.
Bake cookies until lightly golden around edges, rotating pans halfway through, 6 to 8 minutes. Transfer cookies to a wire rack to cool completely.
Before her diagnosis, Caroline wrote a book on cakes called Cake Magic!. She started developing a birthday cake using her gluten-free mix found in that book. Check out other recipes she’s developing for her new life—and the stories behind them—on her blog, The Wright Recipes. Her next book, Catalan Food, written with chef Daniel Olivella, comes out in early September from Clarkson Potter.