Preheat oven to 350°F. Prepare three 8-inch cake pans by lining the bottoms with parchment paper and spraying with non-stick spray.
Beat the butter, oil, and sugars in a large bowl of a stand mixer fitted with the paddle attachment for 2 minutes until light.
1 cup salted butter, 1/3 cup canola oil, 1 cup granulated sugar, 1 cup brown sugar
Add eggs, one at a time, beating on medium-low after each addition and scraping the sides of the bowl as needed.
5 large eggs
Add half of the flour, baking powder, and salt, mixing just until combined.
3 cups + 2 tablespoons cake flour, 2 1/2 teaspoons baking powder, 1 teaspoon salt
Add greek yogurt and vanilla. Mix again just until combined.
1 cup Greek yogurt, 2 teaspoons vanilla extract
Add remaining flour, mixing again to combine. Divide between baking pans.
Bake for 23-25 minutes until a toothpick inserted into the center of the cakes comes out clean.
Cool completely.