Heat the oven to 345°F. Grease an 8-inch round cake pan, line the bottom with parchment, and lightly grease the parchment too.
Make the frosting first so it can set: Place the chopped chocolate and 2 tablespoons of the butter in a heatproof bowl set over barely simmering water. Stir until melted and smooth, then remove from heat and let cool 10 minutes until just warm.
In a mixing bowl, beat the remaining 4 tablespoons butter until creamy. Gradually add the powdered sugar and beat until fluffy, then pour in the cooled melted chocolate and beat until glossy and spreadable. Cover and keep at room temperature while you bake the cake.
For the cake, whisk together almond flour, cocoa powder, coconut sugar, baking soda, salt, and espresso powder in a large bowl, breaking up any almond flour clumps with your fingers or a whisk.
In another bowl, whisk the eggs vigorously for about 45 seconds until slightly foamy. Whisk in the maple syrup and vanilla, then whisk in the apple cider vinegar.
Add the dry mixture to the wet in two additions, folding gently with a spatula until no dry streaks remain. Let the batter rest for 5 minutes to allow the almond flour to hydrate.
Scrape the batter into the prepared pan and smooth the top. Firmly tap the pan on the counter 2–3 times to release air bubbles.
Bake on the center rack for 24–28 minutes, or until the top springs back and a toothpick inserted near the center comes out with a few moist crumbs. Cool in the pan for 15 minutes, then turn out onto a rack and cool completely.
Frost the cooled cake with the chocolate frosting, swirling it across the top. Let it sit 10 minutes to set before slicing.