Preheat the oven to 350 F. Grease and flour a 9-inch cake pan.
Heat the chocolate and oil in a small saucepan over low heat until the edges of the chocolate begin to soften and melt. Remove from the heat and stir until the chocolate is completely melted and smooth. Set aside.
Sift together the flour, cocoa, baking powder, baking soda, and salt into a large bowl. In another large bowl, beat the butter and sugar until light and fluffy with an electric mixer set to high speed, about 3 minutes. Scrape down the sides of the bowl with a rubber spatula. Add the eggs one at a time, beating well after each addition, then beat in the vanilla. With the mixer set to
low speed, add the flour mixture in thirds, alternating with half of the buttermilk and beating each time only until the batter is smooth. Stir in the melted chocolate mixture. Use a rubber spatula to fold in the zucchini.
Scrape the batter into the prepared pan and bake until a tester inserted in the center comes out clean, 35 to 40 minutes. Cool the cake in the pan on a wire rack for 10 minutes, and then turn it out onto the rack to cool to room temperature before glazing.
For the ganache: Bring the cream to a simmer over medium heat in a saucepan. Remove the pan from the heat and add the chocolate and corn syrup. Stir until the chocolate is melted and smooth. Let cool for 3 minutes.
Leave the cake on the rack and set the rack in a rimmed baking sheet to catch the drips. Pour the ganache over the cake, smoothing with a spatula and letting the excess drip down the sides. Let the cake sit until the ganache is set, at least 1 hour. Serve the cake at room temperature.