Over medium-high heat, heat large nonstick skillet or fire up grill.
Trim thin slice off top and bottom of ciabatta bun to create flat surface. Then slice each bun in half horizontally. Lightly spread mayonnaise on outside of ciabatta bun, to enhance browning. Place bun, mayonnaise-side down, on grill or in pan. Top each bun with cheese slice to toast bun and melt cheese.
Season burger with seasoning salt. Grill, broil or pan-fry burger until internal temperature reaches 160°F.
Top burger with caramelized onions. Place burger on one toasted bun, then top with remaining bun. Cut in half and serve with beef broth for dipping.