Preheat the oven to 350°F (175°C). Grease a 9-inch (23 cm) round cake pan.
Melt the butter in a medium saucepan over low heat. Add the sugar and cook, stirring, until the mixture is light brown and bubbly. Pour the mixture into the prepared pan and spread it evenly over the bottom.
Arrange the apple slices in a decorative pattern on top of the butter-sugar mixture. Sprinkle with the cinnamon.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
In a large bowl, whisk together the egg, yogurt, and oil. Add the dry ingredients and whisk until just combined.
Pour the batter over the apples and spread it evenly. Sprinkle with the walnuts.
Bake for 35 to 40 minutes, or until a toothpick inserted in the center comes out clean. Let cool in the pan for 10 minutes, then invert onto a plate and serve warm.
Interesting Facts
Milopita is traditionally served during the Greek Orthodox Easter celebrations.
The Greek word milopita means "apple pie".
Milopita is often served with a dollop of whipped cream or a scoop of vanilla ice cream.