To make the sauce: Combine dressing, sugar, and vinegar in a small bowl. Mix well. Stir in minced onion and set aside. Bring a large skillet sprayed with nonstick spray to medium-high heat on the stove. Place mushroom caps side by side in the skillet, rounded sides down. Cover and cook until soft, about 4 minutes per side.
Place one bun bottom on a plate, and spread with half of the sauce. Top with half of the lettuce (2 tablespoons), followed by the cheese slice. Place one cooked mushroom cap on top, and sprinkle with half of the diced onion (1/2 tablespoon).
Spread the remaining half of the sauce on the other bun bottom, and place it on the sandwich, sauce side up. Top with pickle chips and the remaining 2 tablespoons of lettuce. Top with the remaining mushroom cap and remaining 1/2 tablespoon of onion.
Add the bun top and open wide!