Preheat your oven to 350°F (175°C) and position your rack in the middle for even heat distribution. Measure all ingredients and allow refrigerated items to reach room temperature.
Wash, peel, and core the apples, then cut them into thin slices (about 1/8 inch thick). In a medium bowl, toss the apple slices with lemon juice, 1 tablespoon sugar, and cinnamon. Let the mixture rest while you prepare the batter.
In a large mixing bowl, beat the eggs and sugar for 3-4 minutes until pale and fluffy. Gradually stream in the olive oil while continuing to beat.
Sift together the flour, baking powder, and salt in a separate bowl. Add this dry mixture to the wet ingredients in three batches, alternating with milk. Fold gently using a spatula. Finally, stir in the lemon zest and vanilla extract.
Grease a 9-inch (23cm) springform pan with butter and line the bottom with parchment paper. Pour half the batter into the prepared pan, spreading it evenly to the edges. Arrange half the apple slices in a circular pattern, slightly overlapping them.
Pour the remaining batter over the apples and arrange the remaining apple slices on top in a decorative pattern.
Bake for 45-50 minutes, or until a wooden skewer inserted in the center comes out clean. If the top begins browning too quickly (check at the 30-minute mark), loosely cover with aluminum foil.
Allow the cake to cool in the pan for 15 minutes before releasing the springform sides. If using the optional glaze, warm 2 tablespoons of apricot jam in the microwave for 20 seconds until liquid, then brush over the top of the warm cake.
Before serving, dust with powdered sugar and sprinkle with optional sliced almonds.