With a damp paper towel, wipe any dirt off of mushrooms. Thinly slice the garlic. Rinse and dry collard greens. Cut the thick stem ends off the bunch of collard greens. Stack the greens about 5 leaves high, roll together, and cut into 1 inch thick pieces. Continue for the entire bunch.
Place diced sweet potatoes into a medium pot and cover with water. Bring to a boil, and cook for 20 minutes or until fork tender. Using a measuring cup, reserve 1 cup of the cooking liquid from the pot and set aside. Drain once cooked.
To prepare mushrooms, peel tough skins off of the top. This can be done by grasping the edge between thumb and forefinger and pulling the thin piece of skin back towards the middle of the mushroom. Once all four are peeled completely, score the back of the mushroom 3 times with a knife, about ¼ inch deep and 2 inches long. Rub the mushrooms with 1 tablespoon of olive oil, and season with salt and pepper to taste.
Heat a large sauté pan over medium heat. Add mushrooms top side down. Allow to cook for about 5 minutes, turning when brown and crisp on top. Coat the crisp top with barbeque sauce. Cook for another 5 minutes on bottom side.
Once mushrooms are cooked, remove from heat and set aside. Keep sauté pan on medium high and add 1 tablespoon olive oil and garlic. Cook for 1 minute and add collard greens and red pepper flakes. Sauté collard greens for 3 minutes, tossing to incorporate garlic. Add apple cider vinegar and cook for another 5 minutes, season with salt and pepper to taste. They will be soft and dark green when finished.
To finish sweet potatoes, add them to a food processor, along with brown sugar and vanilla. Pulse until a smooth mixture forms, adding reserved cooking liquid if necessary. To serve, dole sweet potatoes onto plates, topping with collard greens and one portobello cap each. Enjoy!