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, and flip over in pan (marker side down).
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 1/4 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 1/2 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 30 minutes. Remove and store in an airtight container, or serve with fresh berries or ice cream.
To make one full-size Schaum Torte:
Follow the first 4 steps as written. Then, transfer the meringue to a 9-inch buttered spring form pan. Bake at 250 degrees for 1 hour, turn off heat, and leave shell in the oven for 1 hour more (instead of 30 minutes).