Place the apples in an 8-by-8-inch glass baking dish. Spoon the brown sugar into the center of each apple, dividing the sugar evenly among them. Pour the water into the bottom of the dish and bake until tender, about 45 minutes.
Pour the ale and Madeira into a large slow cooker. Put the cloves, allspice, and cinnamon into a small muslin bag or cheesecloth tied with kitchen twine, and add to the slow cooker along with the ginger and nutmeg. Set the slow cooker to medium heat and bring the mixture to at least 120ºF. Do not boil.
Add the egg whites to a medium bowl and, using an electric hand mixer, beat until stiff peaks form. Put the egg yolks into a separate bowl and beat until lightened in color and frothy, approximately 2 minutes. Add the egg whites to the yolks and, using the hand mixer, beat until just combined. Slowly add 4 to 6 ounces of the alcohol mixture from the slow cooker to the egg mixture, beating with the hand mixer on low speed. Return this mixture to the slow cooker and whisk to combine.
Add the cooked apples and the liquid from the baking dish to the wassail and stir to combine. Ladle into cups and serve.