Prep the pan and oven: Heat your oven to 350°F (175°C). Grease a 9-inch round cake pan with butter and line the bottom with parchment. This helps the fruit release cleanly later.

Make the orange topping: Melt 1/4 cup (half the stick) of butter in a small saucepan over medium heat. Stir in the brown sugar and cook 1–2 minutes until glossy and combined. Pour into the prepared pan and spread evenly.

Slice the oranges: Trim the ends, peel the oranges with a knife, removing the white pith. Slice into 1/4-inch rounds. Pick out any seeds. Lay the slices over the brown sugar layer, snugly but without overlapping too much.

Combine dry ingredients: In a bowl, whisk flour, baking powder, baking soda, salt, and optional cardamom or cinnamon.

Cream and build the batter: In a large bowl, beat the remaining 1/4 cup butter with the granulated sugar until sandy and well mixed, about 1–2 minutes. Add the oil and beat another 30 seconds. Beat in eggs one at a time. Stir in vanilla, orange zest, yogurt, and orange juice until smooth.

Finish the batter: Add the dry ingredients to the wet and mix gently until just combined. The batter should be thick but pourable. Don’t overmix.

Assemble: Spoon the batter over the orange slices and smooth the top. Tap the pan once on the counter to remove large air bubbles.

Bake: Place on the center rack and bake 35–45 minutes, or until a toothpick in the center comes out clean and the top is golden. If it browns too fast, tent loosely with foil.

Cool briefly and flip: Let the cake rest in the pan 10–12 minutes. Run a thin knife around the edge. Invert a serving plate over the pan, then flip confidently. Lift off the pan and peel away the parchment.

Serve: Let it cool another 10 minutes to set the caramel. Slice warm or at room temperature. Add a dollop of whipped cream, yogurt, or vanilla ice cream if you like.