In a medium bowl, whisk the confectioners' sugar with the flour and fold in the dates. In a large bowl, beat the egg whites at medium high speed until soft peaks form. Gradually add the granulated sugar and beat at high speed until the whites are stiff and glossy. Using a rubber spatula, fold the dry ingredients into the egg whites. Drizzle one-third of the browned butter against the inside of the bowl and fold it into the egg whites until combined. Repeat with the remaining butter, in two additions. Scrape the batter into the cake pan and smooth the surface. Bake for about 50 minutes, or until the cake is golden and firm. (The cake will rise, then fall when it's done.) Transfer the cake to a wire rack and let cool for 30 minutes. Run the tip of a knife around the edge of the pan to loosen the cake, then invert it onto a cake plate.