Dice the onion, 4 celery sticks, 3 carrots, and 2 bell peppers. Mince the garlic, and cut the braising steak into cubes of 1/2 inch.
Put the Dutch oven on the stove on high heat and melt 3 tbsp of butter. When the butter is melted and stopped bubbling add the beef. Sear the beef for a few minutes until browned, then put aside on your countertop.
Add another 3 tbsp of butter to the Dutch oven, add the vegetables. Bake for a few minutes until they browned a bit.
Add the beef back into the Dutch oven, and add 3 tbsp of all-purpose flour, 2 tbsp of tomato paste, about 3 tbsp of rosemary, and 2 tbsp of thyme. Mix and bake for a few minutes on medium heat.
Add 3 cups of bone broth and put the stew to a simmer for about 3 hours. Keep stirring regularly.
After three hours, transfer the stew to a baking dish or pie plate. Let it sit for 15 minutes so it can slightly cool down.
Get the egg yolk and brush it to the sides of the baking dish or pie plate.
Roll out the puff pastry and lay it over the beef stew, trimming the edges to fit the dish. Cut a few small slits in the center to allow steam to escape. For a decorative touch, you can cut out shapes from the extra pastry and place them on top before baking.
Brush the remainder of the egg yolk over the top of the puff pastry and put the pie in the pre-heated oven. Bake for 30 minutes, or until the pastry is golden brown, on 356 °F (180 °C).
Enjoy!