Let the meat warm up to room temperature before cooking it, about 30 minutes.  Then, toss the chunks of stewing beef with the flour, salt, and pepper until coated.

Heat the olive oil in a Dutch oven over medium-high heat until shimmering, then lower the heat to medium-low.  Brown the beef in small batches, removing the browned pieces to a bowl as you go.  Turn the pieces when they no longer stick to the pan.

Turn the heat back up to medium-high and add the sliced onions and a little of the broth.  Stir and cook the onions for a few minutes, until they have softened.

Add the tomato paste, Worcestershire sauce, mustard, and the remaining broth.  Bundle together the sprigs of fresh thyme and parsley and use kitchen twine to tightly tie them into a bouquet garni.  Add the herbs and bay leaf to the pot and stir well to combine the ingredients.

Bring to a boil over medium-high heat, then turn down the heat to low and simmer for 2 to 2 ½ hours, or until the meat is very tender.

Remove the bouquet garni and bay leaf, then pour the stew into a 6-cup pie dish and set aside to cool.  This step is important, as a steaming hot filling will melt the butter in the puff pastry.  You can even refrigerate the filling overnight at this stage if desired.

Once the stew is no longer hot, brush the edge of the pie dish with beaten egg and cover the filling with the puff pastry.  Press the edges down to seal and trim off the excess pastry.  Brush the whole top with beaten egg and cut several vent holes.

Bake at 400 F for about 35 minutes, or until the crust is well browned.  Let the pie cool for 15 minutes before serving.  Enjoy with mashed potatoes and boiled peas.