Set your oven to 375°F (190°C). Grease a springform pan with butter or line it with parchment paper.
Peel and chop the pears into bite-sized chunks, yielding around 2.5 cups (375 grams). Set aside.
In a large bowl, beat the eggs and sugar together until pale and fluffy. Add the almond extract (if using), vanilla extract, and olive oil, then beat again until well combined.
In a separate bowl, whisk together the almond flour, all-purpose flour, baking powder, and a pinch of salt.
Gently fold the flour mixture into the wet ingredients until just combined.
Carefully fold in the chopped pears, making sure they are evenly distributed throughout the batter.
Pour the batter into the prepared springform pan. Smooth the top, and sprinkle the shaved almonds evenly over the surface.
Place the cake in the preheated oven and bake for about 45 minutes, or until the top is golden brown and a toothpick inserted into the center comes out clean.
Allow the cake to cool slightly in the pan before removing. Finish with a dusting of powdered sugar.