Lightly crush gingersnap cookies and add to food processor. Crumb the cookies with pulse setting of the processor.
Heat the butter to melt in a medium skillet over medium heat. Add the peaches to the skillet and season with salt, add lime juice and saute to soften the slices 6 to 7 minutes. Sprinkle in brown sugar and toss to coat. Season peaches with cinnamon and nutmeg. Spoon peaches into dessert cups and top with small scoops of ice cream, top with ginger crumbles.