Preheat oven to 175°C (350°F). Butter and line a 10-inch springform pan with parchment paper.
Chop the apples into ¼-inch pieces and toss them in 1 tablespoon of lemon juice to prevent browning. Set aside.
In a medium bowl, whisk together the flour, baking powder, sea salt, cinnamon, cardamom, and lemon zest.
In a separate large bowl, whisk the eggs and sugar until frothy. Add olive oil and yogurt, and mix until smooth.
Add the wet ingredients to the dry ingredients, mixing until just combined. Gently fold in the chopped apples until they are evenly distributed in the batter.
Transfer the batter to the prepared pan, smoothing the top with an offset spatula.
Bake for 30-40 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan, then dust with confectioner’s sugar before serving.