Whisk together the flour, dark cocoa powder, baking soda, and salt in a large bowl.
Make a well in the center of the dry ingredients and add to it the white sugar and oil.
Beat with electric mixer to incorporate, then add the vanilla extract, zucchini, and milk. Mix until well-combined and no dry patches remain.
Stir in the chocolate chips with a wooden spoon or spatula.
Scoop batter into pan. Bake for 25-30 minutes (for a 9x13 pan) or 35-45 min (for an 8x8 pan). They're done when a toothpick inserted in the middle comes out clean.
To Make the Chocolate Frosting
Combine the sugar, dark cocoa powder, butter, and milk in a medium saucepan over medium heat. Bring to a boil for 2-3 minutes, stirring constantly.
Remove from heat and stir in the vanilla extract. Let stand for 1 minute, then beat with an electric mixer for 3 minutes to thicken.
Scoop frosting on top of completely cooled brownies and smooth with spatula. Allow frosting to set before serving or storing.
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Notes
Note: Nutrition information is a rough estimate only; actual values will vary based on the exact ingredients used and amount of recipe prepared.