Melt the butter with the olive oil in a heavy pot. Sear the meat over medium-high heat in batches until brown, 4 to 5 minutes; remove to a plate.
Add the carrots, celery and shallots and saute until the vegetables start to wilt, about 5 minutes. Reduce the heat to medium low, add the mustard, garlic and 1 tablespoon of the flour and saute for 1 minute. Add the mushrooms and cook for 2 minutes. Pour in the wine, beef broth and 1 cup water. Add salt and pepper to taste and stir. Bring to a boil. Return the browned meat to the pot and reduce the heat to low. Add the bay leaves and thyme sprigs, then cover and simmer for 30 to 45 minutes.
After 45 minutes, mix the remaining 2 tablespoons flour with a little water and pour into the stew. Cook and thicken for 10 more minutes. Remove from the heat and set aside to cool completely.
Preheat the oven to 425 degrees F.
On a lightly floured work surface, roll out the puff pastry sheets one by one to get rid of the creases. Set a 6- to 8-inch ovensafe skillet upside down on a pastry sheet and cut a circle around it, making it 1/2 inch larger than the dish. Repeat with the remaining 5 skillets using all of the pastry sheets; discard the scraps.
Put the 6 skillets onto 2 baking sheets and fill the skillets with the cooled beef mixture. Sprinkle over some chopped bacon and 1/2 teaspoon chopped parsley on each.
Top each skillet with a pastry circle, pressing along the edges to seal. Mix together the egg and 1 tablespoon water in a small bowl to make an egg wash. Brush each pastry lid with the egg wash. Bake until the pastry is puffed and golden brown, 20 to 25 minutes.