Preheat the oven to 350-degrees F.
In a Dutch oven, heat the olive oil over medium-high heat.
Season the beef with salt and pepper and 2 tablespoons of flour.
Working in batches, brown the beef. Each batch will take 5-7 minutes.
Transfer the cooked beef to a bowl.
Reduce the heat to medium and add the butter.
Cook the onion and carrots until lightly browned. (Mushrooms can be added at this step as well if desired.)
Add the garlic and cook 1-2 minutes.
Stir in the tomato paste and cook 2 more minutes.
Deglaze the pan with the dry red wine (or water). While the alcohol evaporates, scrape the bottom of the pan to get off any flavorful bits.
Mix in the remaining flour and cook 1-2 minutes to get rid of the raw flour taste.
Stir in the beef broth, soy sauce, Worcestershire sauce, dried thyme, dried tarragon and bay leaves.
Add the cooked beef back to the pot along with the potatoes.
Season with additional salt and pepper to taste.
Increase the heat to medium-high and bring the pot to a simmer.
Cover the pot and place the pot into the oven for 1 hour, 20 minutes.
Lightly butter a 9" pie plate.
Remove the pot from the oven and stir in the frozen peas and corn.
Spoon the mixture into the prepared pie plate.
Wewalka's Pie Dough is 9", so there is no need to roll out the dough!
Place the pie dough over the top of the filling.
Firmly crimp the edges and cut several slits to allow steam to escape.
Beat an egg and brush the dough with it.
Bake the pie for 20-25 minutes until the crust is golden brown.
Remove the pie from the oven and cover with aluminum foil to rest for 15 minutes.