To make the candied lemons:

Slice the lemons thinly. Plunge into boiling water for 1 minute to remove bitterness from the skin. Add the sugar and water into a heavy-bottomed pan. Dissolve, stirring frequently. When the sugar is completely dissolved, bring it to a steady boil. Boil for 5 minutes without stirring. Add the lemon and cook for 10 minutes or until translucent/glassy in appearance. Remove the lemon from the syrup with a slotted spoon and spread it into a single layer on a silicone-lined baking sheet. Preheat the oven to 100°C (90°C fan-assisted). Dry out the lemon for 30 minutes.

For the cake:

Preheat the oven to 180°C (160°C fan-assisted). Grease a Le Creuset 26cm Heritage Rectangular Dish and set it aside.

In the bowl of a stand mixer fitted with the paddle attachment, place the sugars, olive oil, lemon zest and thyme and beat until emulsified, about 5 minutes.

In a separate bowl, whisk the dry ingredients together. Add the dry ingredients to the wet mixture with the eggs, alternating, beating until just combined, and continue until all the ingredients are used. Spoon the batter into the prepared dish and smooth the top (the batter should be thick). Bake for 1 hour 30 minutes.

To make the syrup for the cake:

Combine the sugar, water and lemon juice, zest, and thyme. Dissolve the sugar and bring to a boil for 2 minutes, then remove from heat. Pour over the hot syrup and immediately decorate with the candied lemons and thyme sprigs. Serve warm with double-thick plain yoghurt and the reserved syrup from the candied lemons.