Cut the roasted peppers into 1/4-inch wide strips; cut the strips in half.
Heat the oil in a small skillet until hot. Add the onion slices and sauté until golden, about 5 minutes. Add the garlic and oregano; cook 1 minute. Stir in the pepper strips and remove from the heat. Season with salt.
Preheat a gas grill to medium or prepare a charcoal fire, letting coals burn until covered with gray ash and medium-hot.
Remove the stems from the mushroom caps and reserve for another use. Wipe the mushroom caps clean with a damp towel. Spoon about 2 tablespoons of the sauce on the underside of the caps. Distribute some of the roasted pepper mixture over the sauce. Place on the grill then cover the grill and cook until mushroom cap is golden and tender, about 5 minutes. Sprinkle the caps with the cheese; re-cover the grill and cook until the cheese is melted, usually 2 to 4 minutes.
Serve immediately sprinkled with the cilantro.
Makes 6 servings.
Variation: You can substitute 6 small Boboli pizza crusts for the mushroom caps.