Arrange the pastry flour with the brown sugar or brown sugar, the ground almonds, the oat flakes, a pinch of salt and a little finely grated lemon zest in a container. Cut the cold butter into cubes, add and mix with a wire mixer or, better, rubbing with hands until it has a creamy, homogeneous, sticky texture.
Wrap in plastic wrap forming a disk and refrigerate for at least 30 minutes. Meanwhile, preheat the oven to 200ºC and grease a curly cake tin of about 20-22 cm in diameter and let the filling ingredients temper out of the fridge.
Roll out the dough between two layers of non-stick greaseproof paper and cover the mold. It is a sticky dough and becomes soft quickly if it’s really hot, but it doesn’t have to be perfect. With the help of the baking paper and your hands, spread to occupy all the nooks and crannies of the mold and bake in white for 15 minutes (leaving a layer of paper and putting weight on top, such as dried legumes or rice).
Remove the paper and weights and check that it is firm and somewhat golden; if it is very white, bake a few more minutes. Remove, lower the oven power to 160ºC without air and prepare the filling.
Beat together the eggs, cream cheese, yogurt or whipped cheese, sugar, a teaspoon of lemon juice and another of its fine zest, vanilla, another pinch of salt and cornstarch, until smooth. To procure don’t let too many bubbles come out or gently tap the bowl against the table to remove and explode any.
Pour over the cooked cake. Cut the washed figs (peeled optionally) into quarters and distribute in the filling to taste. Bake for about 40-45 minutes, or until set. Let cool a bit before refrigerating for a few hours.