Preheat your oven to 350 degrees Fahrenheit, and set rack in middle position
Combine your flour, ground almonds, baking powder, ground nutmeg and salt in a medium sized bowl. Whisk until well combined and then set aside.
In the bowl of your stand mixer (or in another bowl if you will be using a hand held mixer) combine the egg yolks with the sugar. Beat at medium speed for 3-5 minutes until the mixture is a pale yellow colour. Slowly pour in the oil and almond extract. Beat until well combined.
With your mixer speed on low, carefully add the flour mixture to the mixing bowl containing the egg yolks, sugar and oil. Mix to combine and then add the Greek yoghurt. Be careful not to over mix.
In another bowl, using a hand held mixture, beat your egg whites until stiff peaks form. (See note if you will be using only a stand mixer). Using a rubber spatula gently fold the egg whites into the cake batter.
Grease a 9 inch spring form pan or round cake pan with some vegetable oil, and pour the batter into the pan.
Arrange the peeled and quartered pears in a circular pattern as shown in picture above. Use enough pears so that as much of the top surface of the batter is covered.
Sprinkle the sliced almonds over the pears.
Bake your cake in the middle rack of your oven for 60-65 minutes, until the cake is golden brown on top and a toothpick inserted into the middle of your cake comes out clean. If after approximately 50 minutes the cake is getting too dark on top cover it loosely with aluminum foil.
When your cake is fully baked remove it from the oven. If you are using a spring form pan: Allow your cake to cool for 5 - 10 minutes. Slowly go around the edge of the cake with a knife to loosen it from the sides. Release the sides of the spring form pan from the pan base slowly and lift off. If using a regular cake pan: let your cake cool for 10-15 minutes, and then remove the cake from the pan by flipping it onto a wire rack. Then flip your cake over again as you want your pears and the sliced almonds to be on top.
Dust with icing sugar just before serving it.