Place the milk in a medium bowl and stir in the yeast, then stir in the flour and 2 tablespoons sugar. Stir for 1 minute, then set aside for 30 minutes to 2 hours, whichever is most convenient.
When ready to proceed, add the egg, salt, and melted butter and mix thoroughly. Cover with plastic wrap and let stand for 6 to 8 hours, or overnight. (If keeping the batter for longer than 8 hours, or if the temperature is very warm, refrigerate the batter until 2 hours before using.) The batter should be bubbly when ready.
Before cooking the pancakes, decide which method you wish to use to caramelize the pancakes: If using a broiler, turn on the broiler and use an ovenproof 8- to 9-inch skillet. Otherwise, put out two heavy 8- to 9-inch skillets.
Heat a heavy 8- to 9-inch skillet over medium heat, and melt 1 tablespoon of the butter. Add half the apples and sauté until soft but not brown. Spread the slices well over the bottom of the pan, sprinkle on 1 tablespoon sugar, and lower the heat to medium-low. Pour on a scant 1½ cups batter and spread it to the edges of the skillet. Cook until the top is spongy and dull, no longer liquid and shiny, about 5 minutes (be patient). Meanwhile, if using two skillets, butter the other one lightly and place over medium-high heat.
Sprinkle the top of the pancake generously with cinnamon sugar (about 1 tablespoon). Place the skillet under the broiler and broil until the cinnamon sugar melts, about 1 minute; or flip the pancake into the other skillet and cook for 1 to 2 minutes. Transfer the pancake to a platter apple side up.
Repeat with the second pancake. Serve hot.