Slice and chop all vegetables. Set aside for later.
Cut elk roast in 1 inch cubes. Toss in flour mixture.
Heat olive oil in a dutch oven.
Place meat carefully in hot oil. Fry 2 minutes then turn and fry 2 more minutes on second side. Stir occasionally.
Add vegetables and stir for several minutes until they are beginning to soften. Add Guinness Stout and beef broth, stir up any browned bits on bottom of dutch oven.
Add the frozen peas, Worcestershire sauce, thyme, rosemary, tomato paste, salt, and bay leaves. Stir well.
Place the elk stew in the oven - covered - and bake at 250° for 2½ hours.
Turn oven to 400°. Place pastry crust over the elk stew, and brush with beaten egg. Cut several slits in the crust, and place in the oven. Bake for 30 minutes, uncovered, until crust is golden brown.