Preheat a smoker to 250 degrees F. Add a small amount of wood for flavor; we prefer cherry.
Sprinkle pork shoulder with BBQ rub until completely coated. Place shoulder in smoker and smoke until it reaches an internal temperature of 175 to 180 degrees F, 5 to 6 hours. Let rest for 1 hour. Refrigerate overnight.
Slice pork shoulder into thin deli slices, no more than 1/8-inch thick. (Do not trim off fat; fat is flavor.)
Add 1/4 cup vegetable oil to a large saucepan over medium heat. Add diced onion and saute until translucent, about 5 minutes. Add minced garlic and saute for an additional 2 minutes. Add beef base and 1 quart water and whisk until beef base is dissolved. Reduce to low heat, then add red wine, soy sauce, Worcestershire sauce, basil, oregano and thyme. Simmer for 1 hour. Strain au jus through cheesecloth or a fine strainer to remove particles and then return liquid to saucepan.
Heat a medium skillet over medium-high heat. Add remaining 1/4 cup vegetable oil and heat until hot, then add sliced yellow onion and red bell pepper and saute until softened. Remove to a bowl.
To assemble a sandwich, dip 6 ounces sliced pork shoulder in hot garlic au jus for 1 minute to heat. Transfer to a skillet over medium heat. Add a generous amount of the pepper and onion mix on top. Cover with a slice of provolone and cover pan until cheese is melted, about 30 seconds. Transfer Philly mixture to a hoagie roll with a spatula and serve with a side of the hot garlic au jus. Repeat with remaining ingredients to make 5 more sandwiches.
A meat slicer works great for slicing the pork thin, a sharp slicing knife will work well too.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.