A delicious, decadent cake that happens to have a pretty generous amount of beets and zucchini in the mix. When I served it to my kids, I didn’t tell them about the vegetables. It's not because I was trying to pull one over on them, but because I was curious to see if they'd notice. They didn't. What they did do, was ask for seconds.
Preheat the oven to 350 degrees, with a rack in the lower third. Generously butter a 10-cup bundt pan. Dust the pan with flour, tapping out the excess. (Alternatively, use a 9-by-2-inch square baking pan.)
To make the cake, whisk together the whole-wheat pastry flour, all-purpose flour, cocoa powder, baking powder, baking soda, salt, and cinnamon into a bowl. Set aside.
In the bowl of a standing mixer fitted with the paddle attachment (or with a handheld mixer), beat together the olive oil, butter, granulated sugar, and brown sugar on medium speed until light and creamy, about 4 minutes. Mix in the eggs, one at a time, beating well and stopping and scraping down the bowl after each addition. Mix in the yogurt and vanilla. On low speed, add the flour mixture and beat until nearly combined but still streaky. (The batter will be thick.) Use a wooden spoon or a spatula to stir in the zucchini, beets, and chocolate chips.
Let the cake cool in the pan for 30 minutes. Invert a flat serving plate over the pan and invert the pan and plate together to release the cake. Lift off the pan and let cool completely.