Cook bacon according to package directions; drain, and set aside.
Sprinkle tomatoes evenly with salt and pepper; sprinkle avocado with vinegar.
Stir together butter and Parmesan cheese.
Set aside.
Spread mayonnaise on 1 side of 4 bread slices; layer each with 1 sharp Cheddar cheese slice, 1 tomato slice, 2 avocado slices, 2 bacon slices, 1 Monterey Jack cheese slice, 1 tomato slice, and 1 white Cheddar cheese slice.
Spread remaining 4 bread slices with dressing; place on top of sandwich with dressing side down.
Spread half of butter mixture evenly on 1 side of sandwiches.
Cook 2 sandwiches, buttered side down, in a hot nonstick skillet or griddle over medium heat 2 to 3 minutes.
Spread remaining butter mixture evenly on ungrilled sides of sandwiches; turn and cook sandwiches 2 to 3 minutes.
Repeat procedure with remaining sandwiches.
Notes / Tips / Wine Advice:
* ½ cup guacamole may be substituted for avocado and rice vinegar.