Heat the oven to 350°F and grease and flour a 9-by-9-inch baking pan, or line it with parchment paper for easier lifting.

In a large bowl, stir together the flour, granulated sugar, dark cocoa powder, baking powder, salt, and dark chocolate chips, breaking up any cocoa lumps with the back of a spoon.

In another bowl, lightly beat the eggs, then add the vegetable oil, vanilla extract, sour cream, and finely grated undrained zucchini and mix well.

Add the zucchini mixture to the dry ingredients and stir until just combined; the batter will seem very dry at first, so do not add milk.

Let the batter sit for 5 minutes so the zucchini releases moisture, then stir again until it is noticeably wetter and easier to spread.

Spread the batter evenly in the prepared 9-by-9-inch pan and bake for 35 to 45 minutes, starting to check around 35 minutes, until a toothpick inserted in the center comes out with moist crumbs but not wet batter.

Let the brownies cool completely in the pan before frosting so the frosting does not melt into a chocolate landslide.

While the brownies cool, whisk together the melted butter, cocoa powder, milk, powdered sugar, vanilla extract, and pinch of salt until smooth and creamy, adding a tiny bit more milk if too thick or a little powdered sugar if too loose.

Spread the frosting over the cooled brownies and let it set before slicing; for very clean squares, chill the frosted pan for about 30 minutes first.