For the fig and brown sugar base preparation, start by greasing an 8-inch round cake pan, then add a parchment round to the bottom.
Blend melted butter, brown sugar, and salt, then drizzle it over the parchment-lined cake pan. Ensure even coverage using an offset spatula.
Slice the figs in half, then arrange them with the cut side down on the buttery brown sugar.
To prepare the cake, start by preheating the oven to 350°F using convection (177°C).
In a mixing bowl, blend together flour, baking powder, baking soda, and salt.
Blend eggs and butter thoroughly. Next, incorporate sugar, yogurt, and orange blossom water, and continue beating until well combined.
Combine the wet with the dry, stirring until just combined; expect slight lumps—it's normal. Avoid over-mixing.
Gently pour the batter over the figs, using a spatula to even out the top surface. Bake for approximately 30 minutes. It's ready when a toothpick inserted into the center comes out clean.
Allow the cake to cool for 5-10 minutes in the pan. Then, gently trace around the edge with a butter knife to loosen it. Invert a plate or cake stand over the cake, wearing oven mitts. Hold both the plate and the cake, thumbs under the pan, and swiftly rotate and shake to release the cake. Remove the pan, slice, and serve.