Combine butter, coconut oil, sugar, salt, vanilla extract, vanilla seeds (if using), baking powder, baking soda, and almond extract in the bowl of a stand mixer fitted with a paddle attachment. Mix on low to moisten, then increase speed to medium and beat until fluffy and light, about 5 minutes. Pause to scrape the bowl with a flexible spatula, then beat a minute more.

With the mixer running, crack in the egg and continue beating until smooth. Reduce speed to low, add flour, and mix until dough begins to gather around the paddle but the flour hasn't quite disappeared. Fold once or twice with a flexible spatula to ensure the dough is well combined. Divide in half and proceed to the next step, or wrap in plastic and refrigerate up to 1 week.

When ready to bake, adjust oven rack to lower-middle position and preheat to 350°F (180°C). On a generously floured surface, roll a portion of the dough to a thickness of ¼ inch. Cut with assorted cookie cutters and transfer to a parchment-lined rimmed baking sheet, leaving at least an inch of space in between cookies.

Transfer to oven to bake. For soft cookies, bake until puffed and firm but perfectly pale, about 12 minutes. For crisp cookies, continue baking until pale gold around the very edges, about 3 minutes more. Let the cookies cool to room temperature directly on the baking sheet, about 30 minutes.