Preheat the oven to 350 degrees Fahrenheit and grease a 9-inch springform pan or round cake pan thoroughly.
Whisk together the flour, ground almonds, baking powder, nutmeg, and salt until evenly combined.
Beat the egg yolks with the sugar until pale and fluffy, then slowly mix in the vegetable oil and almond extract until smooth.
Add the dry ingredients to the batter on low speed and stir in the Greek yogurt just until incorporated without overmixing.
Whip the egg whites to stiff peaks in a separate bowl, then gently fold them into the batter using a rubber spatula.
Spread the batter into the prepared pan, arrange the pears on top in a circular pattern, and sprinkle with flaked almonds.
Bake for 60 to 65 minutes until the top is golden brown and a toothpick inserted into the center comes out clean.
Cool the cake slightly before removing from the pan, then dust with icing sugar before serving.