Pre-heat oven to 450F.
Slice the bacon into 1/4 inch wide lengths. Cube beef.
Lightly brown bacon in frying pan. Remove bacon, reserving bacon grease. Reheat the bacon grest until very hot and ude to lightly fry beef cubes just until brown on all sides. Remove beef and set aside with bacon.
Add 1 tsp. olive oil to any remaining bacon grease. Quickly and very lightly fry the sliced carrot and sliced onion.
Place bacon, beef, fried carrots, and fried onions in an oven-safe casserole dish with lid. Add salt and pepper. Sprinkle with flour. Put lid on casserole and vigorously shake to distribute salt, pepper, and flour.
Remove cover, and place the casserole in pre-heated oven on middle shelf. Bake five minutes. Remove casserole, stir ingredients, and return to oven for five more minutes.
Remove casserole from oven. Turn oven temperature down to 325 F. Stir in wine, pureed tomatoes, herbs, mashed garlic, thyme and bay leaf.
Put mixture into a pot, cover, and on the stove-top, and bring to a boil. Quickly remove mixture, return to the casserole, cover the casserole and return to oven for 3 hours.
Near the end of the three hours, heat half of the butter and remaining 1 tsp. olive oil in a small saucepan. Add whole button onions and, over very low heat, sautee for 10 minutes until brown on all sides and soft. Set aside.
Repeat with mushrooms and set aside.
At the end of the meat cooking time, drain with a collander - RESERVING liquid.
Reduce oven temperature to 200 F.
Mix the beef mixture, button onions, and button mushrooms.
Skim any fat from the remaining strained liquid. In a saucepan, boil the liquid until reduced to a medium-thick sauce (test with a spoon. When the sauce coats the spoon, it's done.)
Pour the sauce over the meat mixture in a large pan. Cover and simmer for 3 minutes, stirring to distribute sauce evenly.
Line pie pan with one sheet of puff pastry and brush with one half of beaten egg mixture. Place mixture in a pie pan over puff pastry. Cover with the second sheet of puff pastry. Cut a few small sliced into the top pastry to vent. Brushwith remaining beaten egg. Bake in 200 F oven for 10 minutes until pastry puffs and is golden. Serve immediately.