Mix Korean pepper paste, rice vinegar, sesame oil, soy sauce, sugar, garlic powder and ginger in medium bowl until well blended. Reserve 1 tablespoon of the marinade to toss with grilled vegetables. Place Brussels sprouts and bell pepper in large resealable bag or glass dish. Add remaining marinade; toss to coat well.
Refrigerate 30 minutes. Remove vegetables from marinade. Place vegetables in grill basket. Add mushrooms; toss gently.
Grill over medium-high heat 10 minutes or until crisp-tender and lightly charred, turning occasionally. Remove from grill. Toss grilled vegetables with reserved marinade in large bowl. Sprinkle with sesame seed.