Heat oil in 10-inch skillet; add peppers and onion. Cook over medium heat, stirring occasionally, until peppers and onion begin to soften (6 to 8 minutes). Add mushrooms. Continue cooking, stirring occasionally, until mushrooms are softened (10 to 12 minutes).
Spread foccacia bread halves with mustard; top one half with mushroom mixture and cheese. Cover with top half of focaccia; cut into 8 wedges.