Preheat your grill to medium-high and coat your mushrooms with cooking spray and sprinkle with ground black pepper.
Grill, turning occasionally, until tender, about 12 minutes total.
Meanwhile, mix your mayo, ketchup, and relish in a small bowl.
Transfer your mushrooms to a plate and pat dry with paper towels. Brush with steak sauce and top gills with American cheese and cook until cheese is just melted, about 1 minute more.
Serve on buns with your homemade sauce, spinach or lettuce, and onions/pickles; if using.