Preheat oven to 250˚F. Line two sheet pans with parchment paper. With a Sharpie type permanent pen, trace 6 -3" circles on each sheet of parchment paper.
With an electric mixer on medium-high, beat the egg whites, water and salt till the mixture begins to stiffen and forms a point when beater is pulled out. Continue beating and add, very slowly (over 2-3 minutes), 1 cup sugar, cream of tartar and vinegar.
Add the other 1 ¼ cups of sugar, again very slowly, and vanilla. Beat for 10 minutes on medium speed.
Drop large spoonfuls of meringue onto the circles on prepared sheet pans and hollow out the centers with a teaspoon or follow directions in step 5 for piping.
For piping, snip off a corner of a large zippered plastic bag or decorating bag. Place a large (I use a Wilton 1M) decorating tip into the corner opening. Spoon about ½ of meringue into the bag and twist the top closed. Starting in the center of each circle and moving in a circular pattern fill in each circle with meringue. Continue piping around outside edges, forming walls. I usually go around 2 or 3 more times, depending on how tall I want my Schaum Tortes. Use your finger to smooth out the top where the piping stops.
Place in preheated oven and bake 1 hour, then turn heat off and leave Schaum Tortes in oven for another ½ hour. Remove and store in an airtight container. Believe it or not, these guys also freeze beautifully! I've kept them in the freezer for several months, when thawed you'd never know they had been frozen.