Dough: Whisk the eggs until they are frothy, then whisk in the salt.

Heat the milk to 110F and stir in the yeast and sugar.

Combine the eggs and the bean liquid in the bowl of a mixer. Stir briefly to combine, then with the mixer set on slow, gradually add 3 1/4 cups 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 flour.

Reduce the speed to medium slow and process for 5 more minutes, or until the dough is smooth, very elastic, and clinging to the dough hook.

Gather the dough into a ball. Place in bowl and cover. Allow to rise until doubled in volume; about 1 hour.

Push the top down gently. Separate the dough into 12 to 16 balls, each about the size of a golf ball. Roll the balls into circles, about 5-6 inches in diameter. Place the rounds on a cookie pan, layers separated by foil or waxed paper. Refrigerate them (to stop the rising) until ready to use.

Egg Wash: Combine the beaten egg with the milk.

Filling: To roast the vegetables, if you have a gas range, place the vegetables right on the burner, in a high flame, and roast, turning until the outer skin is charred all around. If your range is electric, you can roast in a preheated 500F oven. Plunge the roasted vegetables into ice water to stop the cooking, then rub off the black skin under running water.

Make the filling by combining the roasted vegetables in a bowl.

Assembly: Brush one side of each round with the egg wash. Divide the filing 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 often, on a griddle or skillet over medium heat (250F) until golden brown.

Per serving: 2533 Calories; 72g Fat (26% calories from fat); 83g Protein; 388g Carbohydrate; 787mg Cholesterol; 2515mg Sodium Food Exchanges: 20 Starch/Bread; 3 1/2 Lean Meat; 8 1/2 Vegetable; 1 Fruit; 1 Non-Fat Milk; 11 1/2 Fat; 1 Other Carbohydrates