In a small bowl, stir together the water, tomato paste, molasses, apple cider vinegar, soy sauce, liquid smoke, and paprika. Set aside.
Coat the bottom of a large skillet with oil and place it over medium heat. When the oil is hot, add the mushrooms in an even layer. Cook for about 5 minutes, flip, and then cook 5 minutes more, until browned in spots. Add the onion and sauté with the mushrooms for about 5 minutes, until very tender. Add the garlic and sauté 1 minute more, until very fragrant.
Add the tomato paste mixture to the skillet and stir to coat the mushrooms. Bring the sauce to a simmer and allow to cook for about 5 minutes, until it thickens up a bit and the mushrooms are very tender. You can add a bit more water if the sauce gets too thick. Season with salt and pepper to taste.
Stuff the mushroom mixture into buns and top with toppings of choice. Serve.