1. Place mushrooms in a sealable bag. Pour marinade from artichoke hearts into the bag, reserving hearts. Seal bag and toss to coat. Let marinate for 30 minutes.
2. Heat oil in large nonstick skillet over medium-high heat. Add peppers and onion and saute, stirring occasionally, until tender, about 16 minutes. Stir in 1/4 teaspoon of the Italian seasoning and the reserved artichoke hearts. Cook until heated through, about two minutes.
3. Meanwhile, heat gas or charcoal grill to medium-hot. Using a long-handled brush, season rack with vegetable oil.
4. Place mushrooms on rack with stem side up and grill, covered, for 3 minutes. Turn mushrooms and grill 3 minutes longer, or until tender. Turn mushrooms again (stem side up) and sprinkle with the remaining 1/4 teaspoon Italian seasoning, salt and pepper. Place a slice of cheese on each and grill, covered, for about 1 minute to melt the cheese.
5. Top each slice of toasted bread with a mushroom. Top mushroom with 1/4 of the pepper-onion mixture and serve immediately. Makes 4 servings.To Broil:
6. Place mushrooms on broiler pan and broil about 5 inches from the heat as directed above in step 4.