BREAD DOUGH: Whisk the eggs in a bowl until they are frothy, then whisk in the salt.
Heat the milk to 110° in a microwave or on top of the stove and stir in the yeast and sugar.
Combine the eggs and the milk mixture in the bowl of an electric food mixer equipped with a dough hook. Stir briefly to combine, then with the mixer set on slow, gradually add 3¼ cups of the flour. Increase the speed to medium and process for 10 minutes. The dough should cling to the dough hook and be fairly elastic. If the dough is soft and sticky, add the remaining ¼ cup flour. Reduce the speed to medium slow and continue to process for 5 more minutes, or until the dough is smooth, very elastic, and clinging to the dough hook.
Flour your hands well, then gather the dough into a ball. Place the dough in a heavy mixing bowl (a thick porcelain bowl is best) that has been lightly sprayed with vegetable spray. Very lightly spray the top of the dough, then put the dough in a warm, draft-free place. (We use the top of our stove, with the oven set at 300°. Or, if you have a gas oven with a pilot light, and you're not using the oven for anything else, put the dough in the unlighted oven, for the pilot light alone generates just enough warmth to encourage rising, and with the door closed, the oven is completely draft-free.) Cover the bowl with a kitchen towel and let the dough rise until doubled in volume, about 1 hour.
When the dough has risen, push the top of the dough down very gently—it will collapse easily. Turn the dough onto a floured surface. With your hands, rolling pin, and working surface well floured, separate the dough into 12 to 16 balls each about the size of a golf ball (the amount of dough produced by the recipe will vary depending upon the hardness of the wheat in the flour and the size of the eggs, among other factors) and roll them out to circles about 5 to 6 inches in diameter. Place the rounds on a sheet pan or cookie pan, layers separated by foil, plastic wrap or waxed paper, and refrigerate them (to stop the rising) until ready to use.
EGG WASH: Combine the beaten egg with the milk.
FILLING: Roast the onions and bell peppers to give them a wonderful, unique flavor. The technique isn't difficult and is very impressive if your company is watching you cook (practice first!). If you have a gas range, simply place the vegetables right on the burner, in the flame, and roast, turning with tongs, until the outer skin is charred all around. If your stove is electric, you can roast in a preheated 500° oven. Plunge the roasted vegetables into ice water to stop the cooking, then rub off the black, charred skin under running water. It should slip right off, but if there are stubborn spots, just remove them with a sharp knife.
Combine the roasted onions and bell peppers in a bowl.
ASSEMBLY: Brush one side of each dough round with the egg wash. Divide the onions, bell peppers and ham among half of the dough rounds with the egg-washed side up, and top with the remaining dough rounds, egg-washed side down. Seal the edges all the way around, coat the outer surfaces with the melted butter, and fry, turning frequently, on a griddle or in a skillet over medium heat (about 250°) until golden brown. Keep the first bread pockets warm while you fry the others, so you can serve everyone at the same time.
Copyright© 1995 by Paul Prudhomme