Position an oven rack to the mid-oven position and preheat the oven to 350°F. Oil the sides of a 9-inch round springform pan, lightly dust with flour. Line the removable bottom with parchment and fasten the sides back accordingly.
Whisk flour, baking powder, and salt together in a medium bowl. Set aside.
Using a handheld electric mixer, beat the eggs on medium speed until foamy, about 1 minute. Add sugar in a slow, steady stream. Increase to high speed until the mixture is fluffy and pale yellow, about 2 minutes.
Reduce to low speed, and while mixer is running, pour the olive oil in a slow, steady stream. Mix until oil is fully incorporated. Add almond flour, milk, lemon zest, and extracts. Beat on medium speed until combined.
On low speed, add the flour mixture and mix until barely incorporated. Stop to scrape the sides and bottom of the bowl if needed. Folding in the flour with a spatula toward the end as necessary, be careful to not over mix. Pour the batter into the prepared pan.
Cut the pear(s) in half lengthwise, core and de-stem. Slice the pear halves into 1/ 8-inch-thick slices. Divide the slices into groups of 4– 5. Arrange into a fan-shape and gently arrange the slices on top of the batter in a decorative pattern, leaving a 1-inch border around outside edge of the pan. Brush the slices with lemon juice. Sprinkle almonds between the arranged groups of pears and around the edge of the pan.
Bake about 50 – 55 minutes. Test for doneness by inserting a toothpick in the center of the cake. It should come out with only a few crumbs clinging.
Transfer the pan to a wire rack and cool for 15minutes. Remove the sides of the springform pan and cool completely before serving.
Optional confectioners' sugar garnish: Before serving, cut a 7-inch circle of parchment paper and lay it over the center of the cake. Sprinkle the confectioners' sugar through a fine mesh sieve around the outer edges.