Position a rack in the center of the oven and preheat to 350ºF.
In the bowl of a stand mixer fitted with the paddle attachment, combine the oat flour, almond flour, cacao powder, tapioca starch, sugar, and salt.
Scatter the butter pieces over the top and drizzle with the dark rum. Turn the mixer to medium-low and run until the dough comes together in clumps and the butter is worked through, 3–5 minutes. (It may seem dry at first, but it will form a dough.)
Dump about half of the crumbs into a 5x13-inch rectangular loose-bottom tart pan (or 9-inch round tart pan) and press evenly into the sides of the pan. Add the remaining crumbs and press evenly into the bottom.
Place the pan on a rimmed baking sheet to catch any drips and bake until slightly puffed and firm to the touch, 20-25 minutes. Remove the crust from the oven and, while it’s still hot, press the sides and bottom with the back of a spoon. This will help it hold together when cool.