Preheat the oven to 350 degrees F.
Line the glass baking dish with parchment paper.
Make the vegan buttermilk: In a glass bowl, combine 1 1/4 cups oat milk and 1 tbsp apple cider vinegar and allow to sit at room temperature (mixture will curdle a bit and this is normal).
Grate zucchini and squeeze out as much liquid as possible.
In a large mixing bowl, whisk together melted vegan butter, sugar, brown sugar and vegan yogurt.
Add zucchini and stir until combined.
Sift in flour, cocoa powder, baking powder and baking soda (do not mix yet).
Add vegan buttermilk mixture and whisk. Before dry ingredients are fully incorporated, add hot coffee and fold batter with a silicone spatula or spoon until just incorporated - do not over mix (the batter will be a bit slippery and slimy; this is normal).
Pour the batter into the prepared baking dish and place in the oven for about 40 minutes or until a toothpick inserted into the center of the cake comes out clean.
Remove cake from oven and allow to cook completely for about 1 hour.
When you're ready to assemble the cake, remove the butter and sour cream from the refrigerator and allow to come to room temperature.
Make the frosting: Using a hand mixer, cream together ½ cup vegan butter until fluffy (about 3 minutes).
Add sour cream to butter and mix again.
Place the vegan chocolate chips and coconut oil into a small glass bowl and microwave in 30-second increments, stirring in between each time, until chocolate is melted and smooth. Allow it to come to room temperature.
Pour the chocolate mixture into the butter and sour cream mixture. Mix until smooth.
Add powdered sugar in 2-cup increments until a frosting consistency is reached, then add cocoa powder and mix until fluffy.
If frosting becomes too stiff, add a bit of oat milk in 1 tbsp increments.
Frost the cake, top with more vegan chocolate chips if desired, and serve!
Leftovers can be stored in an airtight container for up to 3 days.