1. After the deer or elk top round roast has been submerged in the brine for 24 to 48 hours, pull it out and reserve the brine. You can strain and serve it as au jus for dipping the hot sandwiches.
2. The roast can either be cooked using a sous vide water bath or cooked in an oven, barbecue, or pellet smoker.

Sous Vide Instructions

1. Pull the roast from the brine and pat it dry with paper towels. Place the roast in a large vacuum-seal bag with 2 tablespoons of butter. Remove all the air and seal it with a vacuum sealer. You can also place the roast in a large zip-closure bag with the butter and seal it after removing as much air as possible. Just be sure to double bag in case of a leak.
2. Place the sealed bag in a water bath and set the sous vide temperature to 130°F and cook for 12 hours. Be sure the entire bag is submerged. Use a large, heavy bowl to hold the bag under water if needed.
3. After the roast is cooked in the water bath, remove from the bag, making sure to save all the liquid. This will be used for the au jus with the reserved brine. Pat the roast dry with paper towels. Place the cooked roast in the refrigerator covered for at least 3 hours to cool or up to a couple days before slicing it for the sandwiches.
4. Add all the juices to the entire gallon of brine and bring it to a boil over medium heat. Reduce the heat and simmer until the volume of liquid is reduced by 30%. Pour the reduced brine over a fine colander lined with cheesecloth into a large bowl to strain out all the solids. Allow the au jus to cool and then place it in the refrigerator until you are ready to assemble the sandwiches.

Oven, Barbecue, or Pellet Smoker Cooking

1. Pull the roast from the brine and pat it dry with paper towels. Heat the oven, barbecue, or pellet smoker to 350°F. While cooking the roast with one of these methods you will want to catch and reserve any liquid or fat that cooks out of the meat. To do this, place a metal drying rack over a large 9-by-13-inch lipped cooking tray and fill it halfway up with the leftover brine. It's necessary to add the brine to the tray before it goes in the heat so that the drippings don’t dry out at the bottom of the tray in the heat. Cook the roast until it reaches an internal temperature of 125°F. The cook time will vary depending on the size of your roast.
2. Once the roast is up to temperature, remove it from the heat and cover. Place in the refrigerator for at least 3 hours or up to a couple days before slicing to make the sandwiches.
3. Add the tray of drippings and brine to the gallon of leftover brine and bring it to a boil over medium heat. Reduce the heat and simmer until the volume of liquid is reduced by 30%. Pour the reduced brine over a fine colander lined with cheesecloth into a large bowl to strain out all the solids. Allow the au jus to cool and then place it in the refrigerator until you are ready to assemble the sandwiches.

Sandwich Instructions

1. Pour the au jus into a pan and warm it over medium heat on the stove. Slice the meat very thin. This is easiest if you have a meat slicer but it can also be achieved using a large, sharp knife. You will want to slice up the whole roast.
2. In a medium frying pan, heat ½ tablespoon of butter and add the sliced green pepper. Sauté over medium-high heat for 3 to 5 minutes or until the pepper is cooked to your liking.
3. Cut the baguette in sections the length you want each sandwich. Then slice the sections in half lengthwise. Butter both cut sides of the bread and place face down in a large frying pan or on a griddle over medium heat. Cook until the bread is lightly browned.
4. Remove the bread from heat. Place sliced provolone cheese on the bread that will form the bottom of your sandwich. Dredge the sliced meat in the hot au jus and layer it on top of the cheese. Top the meat with cooked green pepper slices, giardiniera pickled vegetables, and the top of the baguette. Serve with a bowl of au jus and a side of pepperoncini peppers.