Preheat oven to 325 F. Generously butter a 9-in. round cake pan (do not use a springform pan as the mixture will leak- trust me). Melt 4 tbsp. unsalted butter over low heat. Stir in the brown sugar. Pour into cake pan and distribute evenly across the bottom of the pan. Sprinkle rhubarb with 2 Tbsp granulated sugar and toss. Place in pan on top of brown sugar mixture. Spread evenly and set aside.
Using an electric mixer, cream softened butter and 1 c. granulated sugar on medium speed until light and fluffy. Add egg yolks, one at a time, scraping down the sides of the bowl after each addition. Beat in vanilla extract.
In a separate bowl, mix the flour, salt and baking powder. Add 1/3 of the flour mixture to the batter in the mixer bowl on slow speed, scraping down the sides and mixing until dry ingredients are incorporated. Add half of the milk-syrup mixture. Continue alternating additions of dry ingredients and milk-syrup mixture, ending with the flour mix.
In a separate bowl, whip egg whites with cream of tartar until stiff peaks form. Fold egg whites into batter in small amounts until well-incorporated. Pour batter into pan on top of rhubarb.
Bake at 325 degrees 40-50 minutes or until the surface springs back to the touch. Let cool for 5 to 10 minutes. Run a table knife around the edges and invert onto a cooling rack. Serve either warm or at room temperature.