Heat the oven to 180C/160C fan/gas 4. Butter a 20 x 22cm ovenproof dish, then pour in the golden syrup and honey. Trim the stalks from the figs, then cut a deep cross in the top, just so they open out a bit, but be careful not to cut all the way through. Sit the figs upright on top of the syrup and put them in the oven to bake for 15-20 mins until softened and starting to caramelise a little at the edges.
While the figs are cooking, make the sponge mixture. Put the eggs, sugar, flour, baking powder, vanilla and butter in a bowl and use an electric whisk to beat until smooth.
Remove the dish from the oven, scoop the figs out with a slotted spoon and set aside. Once the syrup mixture has cooled in the dish, take spoonfuls of the sponge batter and gently place them on top of the syrup. It’s best to do this all the way around the edge first, then end in the middle – this helps keep the syrup mixture separate. Smooth the batter out very gently to cover any gaps and seal the syrup mixture in.
Bake for 35-40 mins or until the sponge springs back when pressed. Allow to cool for around 5 mins or until just warm, then seconds before serving, dot the surface with eight small dollops of the yogurt. Top each mound with a baked fig, then scatter over some thyme leaves and drizzle with extra virgin olive oil, if you like.