Using a spoon, gently scrape the underside of the mushrooms to remove the gills. Trim the underside edges of the mushroom cap to create a flat bottom.
In a large zip top bag, combine the oil, parsley, chives, tarragon and lemon zest and massage to blend. Place the mushrooms in the bag 1 by 1, covering each with the marinade as you add. Let marinate for at least 1 hour (can marinate for up to 24 hours at room temperature).
Preheat a grill to medium. Remove the mushrooms from the marinade, lightly wipe with a paper towel, sprinkle with salt and pepper and place cut-side down on the grill. Cook for 5 minutes, turn and continue cooking until the mushrooms are cooked through, about 5 minutes more. Remove and let rest for a few minutes, allowing the juices to release.
While the mushrooms are cooking, grill the onions and tomatoes until nicely grill-marked and beginning to soften, about 3 minutes per side.
Grill the buns, cut-side down, until toasted, about 1 minute. Spread the buns with a generous amount of Roasted Red Pepper Mayonnaise and layer on the mushrooms, onions, tomatoes and fresh lettuce. Spread the lettuce with additional Roasted Red Pepper Mayonnaise and top off with the grilled bun.
Place the mayonnaise and red peppers into a blender and blend until smooth.