Preheat the oven to 300°F.
Bring a small pot of water to boil over high heat.
Prepare a bowl of ice water.
Trim the fig leaves off their thicker stems; reserve ¼ of the leaves.
Arrange the rest on a sheet pan and toast in the oven until dried and crispy, 16-18 minutes.
While the leaves toast, add the reserved leaves to the pot of boiling water and stir until bright green and slightly softened, 1-2 minutes.
Transfer to the ice water to shock, then squeeze out all as much liquid as possible.
Blend with the olive oil until very green, then strain. Set aside.
Blitz ⅓ of the dried fig leaves in a spice grinder or blender until powdery.
Sift through a fine mesh sieve. You should have about 1 tablespoon of fig leaf powder (a little more or less is ok!).
Adjust the oven temperature to 325°F.
Spray a 9x4-inch loaf pan with nonstick spray; line with parchment and spray again.
Beat the butter and 1 ½ cups granulated sugar together with an electric mixer until fluffy, then beat in one egg at a time.
Mix in the vanilla and salt, then transfer to a silicone spatula and fold in the AP flour, buckwheat flour, starch, and fig leaf powder by hand.
Stir in 2 tablespoons heavy cream.
Scrape into the prepared pan and bake until a tester inserted into the middle comes out clean, about 1 hour.
Let cool completely.
Blitz the remaining toasted leaves and 3 tablespoons granulated sugar in a spice grinder or blender until powdery.
Sift into a bowl with the powdered sugar.
Whisk in 1 tablespoon heavy cream, then a drizzle of water to reach a pourable consistency.
Pour over the loaf cake then let sit to firm up.
Slice and top with yogurt, fig leaf oil, and fresh figs to serve.
