Preheat oven to 350 degrees F (180 C) and line 2 (8-inch) cake pans with parchment paper. Pour aquafaba into bowl of stand mixer and beat until its begins to look light and fluffy (about 3 minutes). Slowly drizzle in cane sugar while beating on high and continue until it forms stiff peaks (it should take about 5 more minutes).

In separate large mixing bowl, stir together the brown sugar, lemon juice, coffee, melted coconut oil, oil, and extract. Add the flour, espresso powder, salt, and baking powder and gently stir.

Remove the mixer bowl from the mixer and use a large spatula to gently fold in the aquafaba into the other bowl of ingredients just until fairly combined. (It's actually better to leave some small lumps then to overmix and lose volume.)

Divide batter into the 2 pans as evenly as possible. Bake for 30-40 minutes until toothpick inserted in center comes out clean and edges are lightly golden. Remove the cakes from oven and cool completely before frosting. (I prefer to cover them and place them in the freezer for at least an hour.)

Beat butter in a large mixing bowl until creamed. Add vanilla, salt, and powdered sugar one cup at a time until incorporated into mixture. Add the almond milk beat until light and fluffy. Melt the white chocolate in a double-boiler or microwave safe bowl, stirring in intervals until completely smooth (it's important not to have lumps of white chocolate especially if you want to use smaller tips.) Pour the white chocolate into the mixing bowl while mixing on low then add the espresso powder and beat until light and fluffy again, about a minute.

To assemble, Gently loosen the cakes form pans by running a thin knife around edges and inverting over plates or trays shake them loose. Use a serrated edge knife to trim and level the cakes if needed. Spread frosting on one of the cakes and layer the second on top. Frost the top and all the sides with remaining frosting until smooth. I did a very basic frosting job and for the trim I didn't even use a tip on my pastry bag, I simply use the open tip of the bag to pipe and decorate a very simple edge. I also added a dusting of cocoa powder and some semi-sweet chocolate chips as a border, but this is optional. Coffee beans would look cute as well.