Preheat the oven to 350℉. Grease an 8-inch baking pan and line the bottom with parchment paper.
In a large bowl, whisk together the ½ cup granulated sugar½ cup brown sugar, ½ cup plain Greek yogurt, ⅓ cup unsweetened cocoa powder, ¼ cup vegetable oil, 2 large eggs, ½ teaspoon baking powder, ½ teaspoon baking soda, and 1 teaspoon fine sea salt until well combined. Add the 1 cup oat flour and stir until just combined. Slowly pour the ⅓ cup coffee into the batter and mix until just combined.
Pour the batter into the prepared pan. Tap the pan on the counter a few times to remove any air bubbles.
Bake for 35-40 minutes until a tester inserted into the cake's center comes out with the tiniest bit of crumb. Transfer the pan to a wire rack and let cool for 20 minutes. Turn the cake out onto the rack, remove the parchment paper, and let cool completely.
Make frosting: In a bowl set over a pot of simmering water, melt the 3 ounces semisweet chocolate and ½ cup unsalted butter until smooth. Let cool slightly, then pour and spread over the top of the cake. The frosting will set as it cools.
Notes
Rest the batter. Oat flour, like all gluten-free flours, needs a little rest so that it can properly hydrate before baking. Let the batter rest in the pan for about 20 minutes, or while the oven heats, for a smoother crumb.
Add espresso. For an extra shot of coffee flavor, whisk in 1 teaspoon of espresso powder to the dry mix. Don't worry - it won't be overwhelming, but will nicely complement the coffee.
Make it dairy-free. If needed, swap the yogurt for non-dairy yogurt and the butter for non-dairy butter.
Use a gluten-free flour mix. When I developed this recipe, I decided to do use y favorite gluten-free flour (oat flour), only. However, you can absolutely use a 1:1 baking mix, or my homemade gluten free flour blend.
Try another icing. Any frosting or icing goes here! See some suggestions in the next section.
Skip the coffee. Don't drink coffee? No worries, you can substitute tea or just hot water instead.