Preheat your oven to 350°F (180°C). Grease a 9x13-inch high-sided sheet pan generously or line it with parchment paper for easy removal.
Make the cake batter: In a large mixing bowl or the bowl of a stand mixer, whisk together the flour, sugar, cocoa powder, salt, baking powder, and baking soda until well combined.
Add the plant-based milk (or plant-based milk and coffee), oil, vegan sour cream or yogurt, vinegar or lemon juice, and vanilla extract to the dry ingredients. Mix with a spatula or the paddle attachment of your mixer until just combined. Avoid overmixing to ensure a tender cake—it's okay if the batter isn't perfectly smooth.
Bake the cake: Pour the batter into the prepared pan and bake for 45–55 minutes or until a toothpick inserted into the center comes out clean. Check a few areas of the cake to ensure even baking.
The cake will rise and may crack, which is normal. As it cools, it will flatten a bit. Allow the cake to cool completely in the pan before frosting.
Make the frosting: In a large bowl or the bowl of a stand mixer, add the vegan butter, powdered sugar, cocoa powder, vanilla extract, salt, and 4 tablespoons of plant-based milk. Beat on medium speed until the frosting is light and fluffy. Add more plant-based milk, one tablespoon at a time, until the frosting reaches a fluffy and spreadable consistency.
Frost the cake: Once the cake has cooled completely, dollop the frosting over the top of the cake. Use a spatula to spread the frosting evenly. Decorate as desired with your choice of vegan sprinkles, chocolate chips, vegan candies, chopped nuts, chocolate shavings, or birthday candles.
Storage: This cake can be covered with plastic wrap or foil at room temperature for up to 3 days or in the fridge for up to a week You can also freeze the cake (frosted or unfrosted) for up to 3 months. When ready to serve, thaw the frozen cake in the fridge or at room temperature.