When you consider blending beans into cake batter as a means of making it better—light and and airy, with a similar crumb to a regular butter and flour cake but with extra moistness and, in the words of Anna, "an almost fudge character"—then you'll want to shout those beans from the rooftop. You'll want to stick a small flag in this cake that says "Made with Beans!" You'll want to tell all your friends!
Because this cake is dairy-free and gluten-free and refined sugar-free, too, it's a great choice to bring to an event with an unknown guest list: Almost everyone will be able to eat and enjoy it (and enjoy it they will).
You won't have trouble making, it either. While the cake lives in the "Investment Cooking" chapter of A Modern Way to Cook, it only fits the bill in the context of the book's other recipes, which are grouped by speed: under 15, 20, 30, and 40 minutes. As cakes go, this one's speedy, with an easy clean-up: The batter comes together in a food processor; the frosting, in a blender.
Preheat the oven to 375° F and grease an 8-inch springform cake pan and line the bottom with parchment paper. Drain and rinse the beans.
In a food processor, purée the beans, honey, and vanilla seeds until smooth. Then add the eggs one by one, pulsing as you go. The batter will rapidly increase in volume—it's fun to watch! Tip this liquidy mix into a large bowl, then add the ground almonds, baking powder, coconut oil, and salt and fold gently to combine. Anna says: "The batter may be a little looser than you'd expect from cake batter, but don't worry."
Pour the mixture into the pan and bake for 30 to 40 minutes. The cake is ready when it's brown on top, firm to the touch, and a skewer comes out clean.
While the cake bakes, make the icing. Put all the ingredients in a blender and blend until very smooth and shiny, 3 to 4 minutes total. Scrape down from time to time as needed. Transfer to a bowl and chill in the fridge as the cake bakes.
Take the cake out of the oven, leave it to cool for 5 minutes in the pan, then release from the pan and cool completely on a rack. Once cool, top with icing and finished with additional lemon zest.