1. Toss mushrooms in bowl with 1 Tbs. olive oil and Classic BBQ Rub. Set aside.
2. Heat remaining 2 Tbs. oil in large skillet over medium heat. Add onions and herbes de Provence, and cook 30 minutes, or until golden, stirring occasionally. Remove from heat, and season with salt and pepper, if desired.
3. Heat grill or grill topper over medium-high heat. Rub grate or grill topper with vegetable oil. Place mushrooms stem-side down on grill. Brush mushroom tops with barbecue sauce, and grill 3 to 4 minutes, or until soft and charred around the edges. Flip, and grill 3 minutes more. Divide cheese among mushrooms, placing in center of each stem side. Grill 1 minute more, or until cheese is melted.
4. Meanwhile, warm buns on grill. Spread barbecue sauce on bottom buns, then top each with 1 mushroom, sautéed onions, and top bun.