Zest the blood oranges, then remove the rinds by slicing off each end of the orange and then cutting the rind away vertically from top to bottom ("supreme" the orange). Thinly slice horizontally into 1/4 inch thick slices and set aside.
In a microwave-safe medium bowl or a saucepan on the stove, melt the butter. Whisk in the brown sugar until it melts.
Grease an 8-inch or 9-inch round cake pan, and line the bottom with parchment if desired. Pour the brown sugar/butter mixture into the bottom of the pan.
Arrange the orange slices on top of the sugar mixture, overlapping slightly, in a spiral pattern. You may wind up not using all the orange slices, depending on their size. Have a snack.
For the Cake:
Preheat the oven to 350 degrees F. In a medium bowl, whisk together the flour, almond flour, baking powder, and salt. Set aside.
In a large bowl, place the sugar and blood orange zest and rub them together with your fingers until the sugar smells fragrantly orange. This releases the oils in the zest and flavors the cake.
Add the olive oil, yogurt, eggs, and almond extract to the sugar and whisk vigorously until the mixture is very well blended.
Add the dry ingredients, and fold and stir them in with a rubber spatula until fully blended and the batter is smooth and thick.
Pour the batter over the orange slices in the cake pan and bake for 35-40 minutes for a 9-inch cake, or 40-45 minutes for an 8 inch cake, until the cake is golden brown and beginning to come away from the pan. A knife or toothpick inserted in the center should come out clean.
Let the pan cool on a wire rack for 5 minutes, then run a knife or thin spatula around the edges of the cake. Place a large plate over the pan, then flip so the cake comes out upside-down onto the plate. Remove parchment, if using.
Let cool to room temperature. Serve alone or with whipped cream.
Notes
*Note: I did not remove the orange rind when taking pictures of this cake because it's prettier that way, but the rinds impart a slightly bitter flavor, so I'd recommend removing them.Storage: baked cake will keep at room temperature for 1-2 days in a tall airtight container that doesn’t touch the blood orange topping. It will keep up to a week in an airtight container in the fridge; microwave slices for 15-20 seconds to reheat. Freezing: baked cake will keep up to 3 months, well-wrapped in plastic and stored in a freezer bag. When ready to serve, allow to come to room temperature for at least 2 hours.Substitutions:
Blood oranges: you can use any other type of orange in place of the blood oranges. Grapefruit might be nice too!
Greek yogurt: you could use sour cream or a plant-based Greek-style yogurt. I have not tested this with non-Greek yogurt and think it would be too wet.
Almond flour: you can substitute almond meal or another 1/4 cup (31g) of all-purpose flour or oat flour instead
Almond extract: you can use vanilla extract instead