Combine first 4 ingredients in a small bowl; brush both sides of mushroom caps with sauce mixture.
Place bell pepper on grill rack coated with cooking spray; grill for 10 minutes or until blackened. Place in a zip-top plastic bag; seal. Let stand 10 minutes. Peel. Place mushroom caps, top sides down, and onion on grill rack coated with cooking spray; grill 4 minutes on each side or until tender. Place 2 cheese slices on top of each mushroom cap; cover and grill 1 minute or until cheese melts.
Spread 1 tablespoon ketchup and 1 1/2 teaspoons mustard over top half of each bun. Place mushroom caps on bottom halves of hamburger buns. Separate onion into rings; arrange onion slices evenly over mushrooms. Top each serving with 1 lettuce leaf, 2 pickles, and top half of bun.
Made more of the Worcestershire sauce because the mushrooms were large, sauce did a good job adding some flavor to the inside of the caps. Otherwise made to recipe, simple but good burgers. Served with coleslaw and corn on the cob.
Used bottled roasted red peppers but otherwise followed directions exactly. It was very good but I wouldn't say it's "worthy of a special occasion" which is I guess what 4 stars mean but it didn't seem right to only give it 3 stars when it was very tasty and I'll definitely make it again.