In a stand mixer bowl, cream together softened butter, coconut oil, brown sugar, and cane sugar until fluffy, about 2 minutes.
Add the eggs and vanilla extract, mixing for 1 minute until smooth and well combined.
Add almond flour, coconut flour, cocoa powder, and salt. Mix on low speed until just combined, then increase to medium for 1-2 minutes until the dough is smooth and uniform.
Form the dough into a ball, wrap tightly in plastic wrap, and shape into a flat disc. Refrigerate for at least 1 hour (or up to overnight).
Preheat oven to 350°F (175°C). Let the chilled dough sit at room temperature for 10 minutes if refrigerated for over an hour. Roll out the dough between two sheets of parchment paper.
Cut out desired shapes. Carefully slide the parchment with the cut-outs onto a baking sheet and freeze for 15 minutes to help them hold their shape during baking.
Transfer the frozen shapes to a parchment-lined baking sheet. Bake for 12-14 minutes, until the edges are set. Let cool on the pan for 3-4 minutes before transferring to a wire rack.
Repeat with remaining dough. Frost or enjoy as is. You've made delicious gluten-free chocolate cookies!