In a microwave-safe bowl, microwave 3 clementines for 3 minutes on high. They will sizzle and pop a lot. Set aside and allow to cool in the bowl for a few minutes.
3 clementines
While the clementines cool a bit, preheat oven to 350°F. Prep a 9-inch circle cake pan with a layer of parchment on the bottom, then spray well with baking spray.
In a 10 cup food processor, zoom the microwaved clementines for 1 minute, scraping the bowl halfway through. The mixture should be pureed, but won't be perfectly smooth.
Add the oil and yogurt, then zoom for 1 minute. Scrape the bowl.
½ cup canola or vegetable oil, ½ cup whole-milk yogurt
Add the sugar, then pulse for 10 seconds. Scrape the bowl.
1 cup sugar
Add the eggs and vanilla, then pulse for 10 seconds. Scrape the bowl.
3 eggs, ½ teaspoon vanilla
Add the flour, baking powder, and salt. Pulse until just combined.
1½ cups all-purpose flour, 2 teaspoon baking powder, ½ teaspoon kosher salt
Pour the cake batter into the prepared pan. Bake for 35-40 minutes, or until a toothpick inserted in the middle comes out clean.