Preheat oven to 425 degrees Fahrenheit. Add red onion, red pepper, mushrooms, and tomatoes to a baking sheet. Combine all dressing ingredients and toss with vegetables, reserving some dressing for drizzling over salad.

Toss cheese with olive oil, garlic powder, salt, pepper, and paprika, and add to baking sheet. Bake for 25 minutes, mixing at least once.

Add lettuce and cucumbers to a large bowl. Add roasted vegetables and cheese, and dress with remaining dressing.