Coat the mushrooms, bell peppers, and onion with cooking spray.
Grill onion, covered with grill lid, over medium high heat(350* to 400*) 8 minutes on each side. Grill mushroom 5 minutes on each side(or you may roast in a 425*F. oven). Place bell peppers on grill, skin side down, and grill 4-5 minutes or until skin is blistered(if you can't find fresh red bell peppers, you can buy them already roasted in jars). See note.
Peel the bell peppers, and cut into strips.
Avocado Mayonnaise: Process all ingredients in a food processor until smooth, stopping to scrape down sides. Cover and chill 2 hours, if desired. Makes 1 cup.
Spread the avocado mayonniase on cut sides of buns: place on cooking grate, and grill 1 minute. Place mushrooms, bell pepper strips, and onion evenly on bottom halves of buns. Top each with avoado slices and top bun halves.
Note: To grill onion, push water soaked skewers crosswise through the whole onion at 1/2" intervals. Slice between skewers and place skewered slcies on grill.