Place a large skillet over medium-high heat with 1 turn of the pan of EVOO, about 1 tablespoon. Add the mushrooms to the pan and cook until golden brown, 7-8 minutes.
Add the onion, garlic and bell pepper to the pan and season liberally with salt and pepper. Continue cooking until the veggies are tender, 5-6 minutes more. Add the tomato paste to the pan and cook 1 minute.
In a small bowl, stir together the brown sugar, vinegar, Worcestershire and tomato sauce. Add the mixture to the skillet and simmer until thickened and saucy.
Pile the Sloppy Veggie Joes onto toasted, buttered bun bottoms and top with pickles and bun tops.