Remove stems from mushrooms. In a large ZipLoc, combine the marinade ingredients and add the mushrooms. Marinate for 1-2 hours.
Prepare the sauce by mixing the sauce ingredients together in a small bowl. Refrigerate until needed.
Cut shallots into thin slices. Add a tablespoon of butter and/or olive oil to a pan on medium heat. Fry the shallots for about 10 minutes or until they're soft and browned, stirring occasionally. You may need to turn the heat down to medium-low so they don't burn. Set cooked shallots aside.
Slice eggplant into 1/2" slices and sprinkle both sides with salt.
Pre-heat grill to high heat. Turn grill down to medium heat once it's ready to go. Grill the mushrooms for about 5 minutes per side until they're cooked through, and grill the eggplant for about four minutes per side or until it's cooked through. To cook the eggplant, place it on the grill and brush olive oil on the top. After four minutes, turn the eggplant and brush the oil on the other side.
If desired, you can toast the insides of the buns. Spread butter on them and then place them on the grill for 30 seconds or until they're toasted as you like... or use the same pan you cooked the shallots in (heat pan to medium-high heat then add the buttered buns and cook until they're toasted as you like).
Prepare other veggies (slice the tomato & avocado).
Spread the sauce on the buns then top with the mushrooms, eggplant, fried shallots, arugula, avocado, tomato, and fresh basil leaves.