Poach the pears
Peel the pears, cut them in half lengthwise and scoop out the cores with a small spoon.
In a saucepan, combine the water, sugar, lemon juice and the vanilla bean (split lengthwise, seeds scraped in). Bring to a gentle simmer, stirring until the sugar dissolves.
Add the pear halves and poach gently for 15 to 20 minutes, until just tender but still firm enough to hold their shape.
Lift out the pears with a slotted spoon, drain them cut side down on paper towels and let them cool. Keep the syrup.
Make the cake
Preheat the oven to 350°F (175°C). Grease a 9-inch (23 cm) springform pan and line the bottom with parchment paper.
In a large bowl, beat the butter and sugar for 3 to 4 minutes, until pale and fluffy. Add the eggs one at a time, beating well after each.
Stir in the yogurt, vanilla extract and lemon zest.
In a separate bowl, whisk together the almond flour, all-purpose flour, baking powder and salt. Fold into the butter mixture until just combined.
Spread the batter in the pan and smooth the top.
Gently press the pear halves into the batter, standing them upright in a ring, evenly spaced, so each slice will get one half. The tops of the pears should stand above the batter.
Bake and rest
Bake for 45 to 50 minutes, until the cake is golden brown and a skewer inserted into the cake (not the pear) comes out clean. If the top browns too quickly, cover it loosely with foil.
Let the cake cool in the pan for 15 minutes, then release the springform and cool completely on a wire rack.
Cover the cake and let it rest overnight. The almond flavor is even better the next day.
Take the cake out of the fridge about 30 minutes before serving. Dust with powdered sugar and serve with whipped cream.
Simmer the leftover syrup until it thickens slightly and serve a small spoonful alongside.