MUFFIN CUPS (first eight ingredients): Whisk the eggs in a bowl until they are frothy, then whisk in the salt.
Heat the milk to 110°F 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°F. 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. 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. Push the top down very gently-it will collapse easily.
Take a piece of dough roughly the size of a golf ball, flour it on all sides, and place it on a floured surface. Gently roll the dough out, working one direction at a time and rotating, turning and flouring the dough frequently. When the dough is circular in shape and very thin, it is ready. Be sure that the thickness of the dough is even, especially at the edges.
Fold the circle of dough in half, then in half again, and drop the point into a cup of a muffin tin. Unfold the circle and, keeping the edges as even as possible, arrange the edges into a decorative, crinkly shape. Repeat with the remaining dough, and put the tin into the refrigerator to keep the dough from rising while you prepare the filling.
ANDOUILLE FILLING (rest of the ingredients): To make the Seasoning Mix combine the Vegetable Magic®, ground dried Chipotle chile peppers, ground allspice, fenugreek, mace, and dry mustard in a small bowl.
Heat a 4-quart pot over high heat for 4 minutes. Add 4 tablespoons of the butter, and the Andouille, onions, bell peppers, celery, and Seasoning Mix and cook, stirring frequently, until the mixture begins to stick to the pan bottom, about 10 minutes. Add ½ cup of the stock and scrape to loosen the brown bits. Sprinkle the flour evenly over the mixture and stir until the white of the flour is no longer visible. Continue to cook, stirring constantly, until the mixture begins to stick to the pan, about 3 to 4 minutes. Add the remaining stock, scrape the pan bottom thoroughly to loosen any brown bits, and cook, scraping the pan frequently, for 10 minutes.
Preheat the oven to 325°F.
Melt the remaining butter. Divide the Andouille filling evenly among the cups and break 1 egg on top of each. Brush the edges with the melted butter and bake until the edges are browned and the filling is heated through, about 15 to 20 minutes. Serve piping hot, and if you should happen to have leftovers, freeze them to enjoy another time.