Leftoverture is a method of adding more crushed grain to already mashed grains and mashing again. It is a cost effective way to experiment with mixed fermentation sours. Usually 9# of base malt is enough to get you > 1.050 OG when you consider "leftover" sugars from the previous mash.
The first time Leftoverture was used as a term in brewing was November 2013 by Matt Warise and Ryan Steagall. They mashed and brewed a 1.120 OG Russian Imperial Stout (RIS). 8 lbs of Pilsner Malt was added to the already mashed grains for the RIS where it was mashed and sparged again. The completed wort was inoculated with White Labs Roesalare Blend. Several months later 32 oz of cranberry juice was added along with Crooked Stave Artisan Beer Project dregs.