Preheat the oven to 350° F. Grease a 9x13 baking dish, and set aside.
Sift the flour, sugar, cocoa, baking soda, baking powder, and salt into the bowl of an electric mixer fitted with a paddle attachment. Mix on low speed until combined.
In a separate large bowl, combine the butter, oil, eggs, sour cream, and vanilla. Whisk until smooth.
With the mixer on low speed, slowly add the wet ingredients to the dry. With the mixer still on low, add the coffee, and mix until just combined.
Turn off the mixer, and use a spatula to fold in the zucchini and chocolate chips.
Pour the batter into the prepared baking dish.
Bake 40-45 minutes or until a toothpick can be inserted into the center and comes out clean. Set aside to cool.
In the meantime, prepare the frosting by adding the heavy cream to a microwave-safe bowl. Microwave on high for 1 minute or until hot. Add the chocolate chips, and let stand for 1-2 minutes.
Whisk the mixture together until the chocolate is completely melted and the ingredients are well combined. Stir in the vanilla and espresso. Set aside to chill for 20 minutes.
Spread the frosting evenly over the cake. Slice, and serve.
Store covered at room temperature for 2-3 days or in the fridge for up to 5 days.