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.