To make the dough, combine the milk, yeast, 2 tablespoons of the sugar and 2 tablespoons of the flour in a large mixing bowl. Mix well and set aside for 30 minutes. In another bowl combine the egg, butter, salt, sugar, and flour. Mix together until smooth and elastic, then combine with the other dough. Do not overmix. Cover and let rise for 1 hour.
For the filling, place 1 tablespoon of butter in a skillet over medium heat. Saute the garlic, crab, tomato, and salt and pepper to taste, for 2 minutes. Remove from the heat and allow to cool. Pour off any excess liquid, then mix well in a bowl with the remaining butter, herbs, shallots, and salt and pepper.
Divide the dough into 12 equal portions, forming them into round balls. On a lightly floured surface, roll each ball out into a 6-inch circle.
Divide the filling into 12 equal portions, placing one portion onto each circle of dough. Take up the edges of each dough circle and roll it into a ball, sealing in the filling. Place on a buttered baking pan, cover with a damp towel, and allow to rise for 25 minutes. Lightly brush with the beaten egg, then bake in the oven for 20 minutes or until golden brown. Serve immediately.