Combine all-purpose flour and Caveman Rub in a medium-size bowl.
Add diced game (venison, elk, or other game) and mix together by hand to ensure all sides of the meat are coated.
Heat olive oil in Dutch oven over medium-high heat until oil is hot.
Add the flour-coated game to the Dutch oven and sear all sides of the beef until just browned. Using a slotted spoon, remove the game meat and set aside in a small bowl.
Add the onion, carrot, celery (collectively called a mirepoix) to the Dutch oven and stir frequently until the onion begins to turn translucent.
Add the Guinness beer and beef broth to the Dutch oven and stir, scrapping the browned bits (called the fond) off of the bottom of the Dutch oven.
Add the Dijon mustard, tomato paste, and Worcestershire sauce to the Dutch oven and stir until fully incorporated.
Add the salt, pepper, thyme, and bay leaf and gently stir (don't break up the bay leaf) until fully incorporated.
Stir the mixture until it begins to simmer. Turn the heat down to low and add the game (and any juices it released) and the diced potatoes into the Dutch oven. Gently stir to incorporate.
Cover the Dutch oven and gently simmer for 3-4 hours, stirring periodically, until the liquid has thickened to almost a gravy consistency. Be sure to avoid breaking up the potatoes when you're stirring. Note: I test the thickness by using the back of a spoon.
Once the liquid has thickened and the game is almost fall-apart tender, remove the Dutch oven from the heat and let the mixture cool fully (at this point you can also refrigerate the mixture over night).
Once the mixture is fully cooled and set (note: see how the spoon stands upright on its own), preheat oven to 400 degrees.
When the oven reaches temperature, add the mixture to the prepared pie crust and spread the contents equally in the pie dough.
Cover with the top half of the pie dough and seal the edges.
Whisk together egg and 1 Tbsp of water to make an egg wash. Use a pastry brush to lightly coat the pie crust.
Using kitchen shears or a sharp knife, cut a "x" into the center of the pie to allow steam to escape during baking.
Place the pie on the middle rack of the oven and bake at 400 degrees for 15 minutes.
Turn the oven down to 375 degrees and rotate the pie in the oven (to ensure even browning). Bake for 45 minutes until the pie crust is golden brown and the pie's internal temperature is 140-150 degrees.
Remove the pie from the oven and let cool for 10-15 minutes so the pie can set. Cut and serve.