Preheat the oven to 350 F. Grease and flour a 9 x 13 baking pan, or line with parchment paper.
Combine flour, sugar, cocoa powder, espresso powder, baking soda, and salt in a mixing bowl, stir to evenly combine.
Combine the zucchini, butter, eggs, and vanilla in a food processor and pulse until smooth.
(Alternatively, if using shredded zucchini, combine butter, eggs, and vanilla in a mixing bowl. Leave out the zucchini for now.)
Spoon the wet mixture into the dry and stir until just incorporated. Fold in the walnuts (and shredded zucchini, if using).
Transfer the mixture to the prepared baking pan and bake until the brownies spring back when gently touched, about 25-30 minutes.