Unsalted butter, for the pan
1 1/2 cups all-purpose flour, plus more for the pan
1/2 cup plus 1/3 cup semisweet chocolate chips
1/4 cup unsweetened cocoa powder (not Dutch process)
1/2 teaspoon kosher salt
1/2 teaspoon baking soda
1/4 teaspoon ground nutmeg or allspice
1 1/4 cups sugar
1/2 cup plus 1 teaspoon extra-virgin olive oil
2 large eggs
1/2 teaspoon vanilla extract
1 medium zucchini, grated and squeezed dry
1 teaspoon honey
Preheat the oven to 350 degrees F. Butter the bottom and sides of a 9-inch-square cake pan. Dust the pan with flour, tapping out the excess.
Toss 1/2 cup chocolate chips with 1 tablespoon flour in a small bowl. Whisk the remaining flour, the cocoa powder, salt, baking soda and nutmeg in a medium bowl; set aside.
Beat the sugar, 1/2 cup olive oil, the eggs and vanilla in a large bowl with a mixer on medium speed until smooth and pale, about 3 minutes. Add the flour-cocoa mixture; beat on low speed until combined, about 2 minutes (the batter will be thick). Add the zucchini and beat until combined, about 2 more minutes. Fold in the flour-coated chocolate chips with a wooden spoon.
Transfer the batter to the prepared pan and bake until a toothpick inserted into the center comes out clean, 30 to 35 minutes. Transfer to a rack and let cool completely.
Make the glaze: Combine the remaining 1/3 cup chocolate chips, 1 teaspoon olive oil and the honey in a microwave-safe bowl. Microwave on medium-high power in 30-second intervals, stirring, until the chocolate is melted. Spread over the cake, then cut into pieces.
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