Combine the ginger and milk in a saucepan. Bring to the scalding point, then remove from the heat and set aside to infuse while preparing the caramel.
Place the first measurement of sugar and the lemon juice in a thick-bottomed saucepan. Place over medium heat and stir constantly with a wooden spoon until the sugar melts and caramelizes to a rich brown color. Immediately plunge the bottom of the pan into cold water to stop the caramelization.
Pour a ⅛-inch (3-mm) layer of caramel on the bottom of 16 soufflé ramekins, 3¼ inches (8.1 cm) in diameter, or in coffee cups with straight sides. Set the forms aside.
Reheat the milk to the scalding point. Whisk together the remaining sugar and eggs. Gradually add the hot milk to the sugar mixture while whisking constantly. Strain the custard and discard the ginger.
Place the forms in a hotel pan or in another suitable pan. Fill the forms almost to the top with custard. Add hot water to the larger pan to reach about three-fourths of the way up the sides of the forms. Move the pan to the oven. Fill each form to the top with custard.
Bake at 350°F (175°C) for approximately 35 minutes or until the custard is set. Let cool completely, then refrigerate for a minimum of 4 hours.
Unmold and serve as directed in Step 6, page 762. Tropical fruits and Layered Florentina Squares make nice accompaniments to these custards.