Rinse the chard under cold water in a colander. Shake off excess water, leaving some still clinging to the leaves.

Heat the olive oil in a large skillet over medium-high heat. Add the shallots and cook, stirring often, for 2-3 minutes. Add several big handfuls of chard to the pan and stir to wilt it down. Continue adding more chard, a few handfuls at a time, until all of it fits into the pan. Cook the chard for 1-2 minutes until bright green and entirely wilted. Remove from heat and stir in the currants, vinegar, and nutmeg, to taste. Season to taste with salt and pepper before serving.