Preheat oven to 350°F. Line an 8x8-inch square baking pan.
In a medium sized mixing bowl, sprinkle ¼ cup cocoa powder over 1 cup hot coffee, stir, and allow cocoa to "bloom" for a few minutes.
Whisk together remaining dry ingredients—½ all-purpose flour, 1 cup brown sugar, ½ teaspoon salt, 1 teaspoon baking soda—in a medium bowl.
To the bowl with coffee and cocoa powder, add remaining liquid ingredients—⅓ cup avocado oil, 1 tablespoon vanilla extract, 1 tablespoon apple cider vinegar—and whisk together.
Add liquid ingredients to dry ingredients and whisk together until well combined.
Pour Vegan Chocolate Cake batter into baking pan.
Bake at 350°F for 30-35 minutes, until a toothpick inserted in the center comes out clean.
Cool in pan for 10 minutes. Lift cake out of pan using parchment paper and cool completely on a wire rack.
Make Vegan Chocolate Icing
Combine 1 cup powdered sugar, 2 tablespoons cocoa powder, and 1 teaspoon vanilla extract to a bowl. Add water 1 tablespoon at a time, stirring until the icing is thin enough to spread.
Pour icing onto completely cooled cake and spread.
Nutrition information based on 1 piece, unfrosted, when cake is cut into 9 pieces.Icing adds 56 calories, 0.1 g protein, 0.1 g fat, and 0.2 g fiber per serving.