Prepare marinated mushrooms: Combine first 6 ingredients in a large zip-top plastic bag. Add the mushrooms; seal and marinate in refrigerator 15 minutes.
Preheat oven to 350°.
Prepare stuffing: Heat oil in a large nonstick skillet over medium-high heat until hot. Add bell peppers and onion; sauté 3 minutes. Combine bell pepper mixture and bread cubes in a large bowl; stir in Jack cheese, parsley, water, and eggs. Drain mushrooms; discard marinade. Place mushroom caps, stem sides up, on a baking sheet. Spoon 1 cup stuffing into each mushroom cap, and sprinkle each with 1 1/2 teaspoons Parmesan cheese. Bake at 350° for 25 minutes or until lightly browned and mushrooms are tender.