Thinly slice the venison and place in a ziploc bag with olive oil, Worcesershire sauce, liquid smoke, and black pepper. Let marinate for one hour.
Set broiler on high.
Add 1 tablespoon of butter to a saute pan set over medium heat and add green peppers when melted. Let green peppers cook for 5 minutes, or until tender-crisp. Remove from skillet, saute the onions and mushrooms until tender.*
Set aside peppers, mushrooms and onions and add the second tablespoon of butter to the skillet. and turn up the heat to medium-high. Add venison and spread out evenly in the pan. Let cook until the underside is seared, then flip and repeat. Continue cooking until meat is no longer pink and is nicely browned. Taste for salt and light salt as needed.
Lightly toast the interior of the hoagie rolls in a separate skillet, toaster, or under the broiler.
Assemble the sandwich by adding half of the meat into each hoagie and topping generously with pepper, onions, mushrooms, two slices of cheese and a smear of mayo.
Place sandwiches briefly under broiler to melt the cheese, approximately for one minute. Be sure to watch the sandwiches, as they will burn quickly.
*All of the vegetables can be cooked together, but peppers take the longest to cook and will need a headstart, or you will have to pick the other vegetables out as they finish cooking.