In a large skillet, saute the precooked beef and pork cubes, onions, and garlic in the butter over high heat for 5 minutes, until the onions are golden brown. Add the red wine to deglaze the pan, loosening any browned bits on the bottom of the pan with a wooden spoon. Add the mushrooms, basil, parsley, thyme, salt, and pepper and cook until the liquid has evaporate. Stir in the demi-glace and cook about 5 minutes more, until all liquid has evaporated again. Remove from the heat. Spread the mixture out onto a baking sheet and let it cool for 10 minutes. Refrigerate the mixture about 1 hour to cool completely.
Preheat oven to 450 degrees. On a lightly floured surface, roll out the puff pastry to 1/8-inch thickness. Cut out 6 (6 to 8-inch) squares and brush the edges with the egg mixture. Place 1 cup of the meat mixture in the center of each square. Fold each square over diagonally to form a triangle and press the edges firmly to seal. Using a fork, gently prick the center of each triangle to allow steam to escape. Lightly brush the edges again with the egg mixture.
Arrange the triangles 2 inches apart on a greased baking sheet. Bake for 8 to 10 minutes, until golden brown.
Preheat oven to 350 degrees. In a small bowl, mix together the oil, salt, and pepper. Rub the oil mixture over the meats. Roast the pork shoulder about 1 hour. Roast the beef chuck about 1 1/2 hours, until a meat thermometer registers 170 degrees for each meat. Remove the meats from the oven and let cool for 20 minutes. Cover and refrigerate up to one day or until ready to use.