Preheat the oven to 350 degrees. Grease an 8 inch round cake pan with butter.
Combine the melted butter, 1/2 cup granulated sugar, brown sugar, and the rhubarb in a bowl, then spread the mixture onto the bottom of the prepared cake pan.
Sift flour, remaining 1 cup sugar, baking powder, and salt together in the bowl of an electric mixer. Add the butter in tablespoon sized chunks, milk, vanilla, and lemon zest. Beat on medium high speed for 2 minutes. Scrape the sides of the bowl. Add the egg and beat an additional 2 minutes, scraping the bowl occasionally. There may still be small lumps of butter, the size of a pea or smaller, in the batter.
Pour the batter over the rhubarb. Bake until toothpick inserted in the center comes out clean, about 45-50 minutes. If the cake is looking too brown at the 35 minute mark, cover it with a sheet of foil.
Allow the cake to cool for about 5 minutes then loosen the sides by running a knife around the edges. Place your cake plate on top of the pan then use your hands to sandwich them together and flip the pan over onto the cake plate. Carefully lift the cake pan off the cake and allow the topping to run over the sides. Serve warm with ice cream.