Preheat oven to 170°C and prepare a 26cm by 21cm baking tray
Add apple pieces to tray and toss with 1 tsp cinnamon powder
Heat a large frying pan to medium heat and add 3 tbsp brown sugar, 2 tbsp olive oil, salt, and vanilla
Allow to melt together for 20 seconds before adding apple pieces to caramelize on one side
Reduce heat slightly and turn apples over when golden to color other sides, cooking for about 5 minutes total
In a bowl, whisk together olive oil, brown sugar, maple syrup, and eggs with yolks
Stir in ground almonds, flour, baking powder, bicarbonate of soda, salt, and lemon zest
Mix in Greek yogurt, almond extract, and vanilla extract
Add baking paper to the tray and scrape in the batter
Scatter caramelized apple pieces evenly over the batter
Bake in the middle of the oven for 40 minutes or until a skewer comes out fairly clean
While the cake bakes, return to the frying pan and add all syrup ingredients: lemon juice, brown sugar, thyme leaves, vanilla extract, salt, and olive oil
Bring to a gentle heat and mix together to form a thick caramel syrup for 15 seconds, then turn off heat
Pour the syrup over the hot cake and allow to soak in
Serve cake warm or at room temperature with crème fraîche or yogurt
