Preheat the oven to 325 degrees F. Stir the sugar and 2 tablespoons water in a medium skillet. Bring to a boil over medium-high heat and cook, swirling the pan but not stirring, until deep amber, 5 to 7 minutes. Pour the caramel into a shallow 10-inch-round cake pan, tilting the pan so the caramel evenly coats the bottom.
Bring a kettle of water to a boil. Whisk the eggnog and eggs in a large bowl until smooth, being careful not to beat in too much air. Pour the eggnog mixture over the caramel in the pan, then place in a large roasting pan. Fill the roasting pan with enough boiling water to come halfway up the side of the cake pan.
Loosely cover the roasting pan with foil and bake 1 hour. Remove the foil and continue baking until the custard is set but still quivers, 40 minutes to 1 hour.
Remove the flan from the roasting pan and let cool to room temperature, then cover and refrigerate until cold and set, about 2 hours. To serve, run a thin knife around the edge of the flan, place an inverted flat plate over the pan and flip to unmold.