Preheat the oven to 375 degrees F. Adjust oven rack so that it’s right under (but not right in) the center. Line the bottom of the angel food cake pan with a ring of parchment. You can skip this step, but it makes it easier to dislodge the cake.Grind the granulated sugar in an old coffee grinder or mini food processor. This makes for a tighter crumb, but you can skip it if you don’t have a grinder.Sift the cake flour and confectioners’ sugar together. Set aside.In the bowl of a stand mixer fitted with the whisk attachment, beat the egg whites just until foamy, then add the cream of tartar and continue beating until peaks are almost stiff. With the mixer still going, add the salt, then gradually add the sugar and continue beating until sugar is absorbed. Beat in the extracts.Turn the mixer to the lowest speed and gradually pour the flour into the side of the stand mixer bowl, being careful not to deflate the whites.
Remove mixer from stand and with a scraper, fold in any flour that didn’t get blended in with the rest.Scrape the cake batter into the pan and bake for 45 minutes or until the top is browned and cake springs back lightly when touched. Turn the cake pan upside down and invert onto its legs to cool for about two hours.When the cake is completely cool, run a regular non-serrated knife around the edges of the cake pan and stem. Unmold the cake and pull off the parchment. Make the Seven Minute Frosting.
Combine the egg whites, sugar, water, cream of tartar and corn syrup in the top of a double boiler and set it over simmering water. With a handheld mixer, beat on high for 7 minutes or until soft peaks have formed and mixture is 160F on a candy thermometer.
Remove from heat. Beat in salt and vanilla and continue beating off heat for about 3 minutes or until peaks are stiff and icing is easy to spread.
