To prepare topping: Coat a 10-inch ovenproof skillet (such as cast-iron) with cooking spray. Add corn syrup and butter; heat over low heat until butter has melted, swirling the pan to coat the bottom evenly. Remove from the heat; spread brown sugar evenly over the bottom of the pan. Sprinkle nuts over the sugar and arrange rhubarb, rounded sides down, in a circular pattern on top. Set aside.

To prepare cake: Preheat oven to 375 degrees F. Combine flour, nuts, baking powder and salt in a food processor or blender; process until finely ground.

Beat 2 egg whites in a large bowl with an electric mixer on high speed until soft peaks form. Gradually add 1/3 cup brown sugar, beating until stiff and glossy. Set aside. (It is not necessary to wash beaters.) Beat whole eggs with the remaining 1/3 cup brown sugar in another large bowl on high speed until thickened and pale, 3 to 5 minutes. Blend in orange zest and vanilla.

Whisk one-fourth of the beaten whites into the whole-egg mixture. Gently fold in half the flour mixture. Fold in the remaining beaten whites, followed by the remaining flour mixture. Spread the batter evenly over the rhubarb.

Bake the cake until the top springs back when touched lightly, 25 to 30 minutes. Let cool in the pan on a wire rack for 5 minutes. Loosen the edges with a knife. Invert a serving platter over the cake. Using oven mitts, grasp platter and skillet together and carefully flip them over. Let the skillet sit for a few minutes to allow any caramel clinging to it to drip onto the cake. Remove the skillet. Let the cake cool for at least 20 minutes. Serve warm or at room temperature.

MAKE AHEAD TIP: Equipment: 10-inch ovenproof skillet (This cake can also be baked in an 8-inch-square glass baking dish. Heat corn syrup and butter in a small pan and brush over the bottom of the baking dish. Bake the cake for 30 to 35 minutes.)