Preheat the oven to 375 degrees Fahrenheit. Prepare two eight or nine-inch cake tins by lining the bottoms with parchment paper and then greasing and flouring them. It helps to add a touch of cooking spray before you place the parchment paper into the tin to help it adhere.
Sift the flour, baking powder, baking soda, salt and cocoa powder into a large bowl or the bowl of a stand mixer. Whisk to mix.
Dump in the remaining cake ingredients--vegan yogurt, water, vinegar, vegetable oil, sugar, pure vanilla extract and cofee, if using.
Whisk for a few seconds, scrape the sides and bottom of the bowl with a spatula, and continue mixing for just a few more seconds until you have a smooth batter. Don't overmix.
Divide the batter equally between the two cake pans. Place in the preheated oven and bake 25-30 minutes or until a toothpick in the center comes out clean.
Let the cakes cool in the pans for around 30 minutes, then slide a knife along the sides to loosen, invert each cake into a plate, turn right side up, and continue cooling on the rack. These cakes are fairly sturdy but always be careful when handling baked cakes, especially if you are new to this.