Preheat grill to medium-high heat (350° to 400°). Combine first 5 ingredients in a large bowl. Add sirloin, stirring until combined. Shape mixture into 4 large patties. Chill until ready to cook.
Grill onion slices on well-greased grill grates 4 minutes on each side. Grill buns, cut sides down, 1 minute or until toasted.
Grill patties 5 minutes; carefully turn, and grill 3 more minutes or until desired degree of doneness. Top each patty with 1 cheese slice during last 1 minute of grilling time.
Top bun bottoms evenly with tomato slices, burgers, avocado slices, grilled onions, and pickled jalapeño slices. Spread bun tops with mayonnaise, if desired.
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