Preheat the oven to 350 degrees and grease a 9-inch cake pan. Prepare the first half of the caramel/rhubarb layer: In a medium saucepan, cook 1/2 cup of the brown sugar over medium heat, stirring frequently, for 3 to 4 minutes or until an amber caramel has formed. Add 4 tbsp of the butter and cook, stirring constantly until combined, 1 to 2 minutes. Immediately pour caramel mixture into the prepared cake pan, spreading to cover the entire bottom of the pan. Arrange the rhubarb in a circular pattern so that it covers the caramel and the bottom of the pan.

Make more caramel sauce: Melt the second 1/2 cup of the brown sugar in a saucepan over medium heat, stirring frequently, for 3 to 4 minutes or until an amber caramel has formed. Add the remaining 4 tbsp of butter and cook, stirring constantly until combined, 1 to 2 minutes. Drizzle the sauce over the arranged rhubarb (it does not have to be perfect). Set the prepared pan aside. It's OK if the caramel starts to harden.

In a small bowl, mix together the flour, baking powder and salt. In a medium bowl, whisk together the brown sugar, melted butter, eggs, and yolks. Fold the dry ingredients into the wet and stir gently to form a smooth batter. Pour the batter over the rhubarb in an even layer in the cake pan, smoothing with a spatula as necessary.

Bake until the top of the cake is golden brown, approximately 35 to 40 minutes. Remove the cake from the oven and let it slightly cool on a wire rack for 10 minutes.

After 10 minutes, gently run a knife or spatula around the edge of the cake to loosen it. Gently invert the cake onto a plate. Serve warm or at room temperature.