Toss avocado wedges gently with Italian dressing; drain well, reserving dressing.
Spread mayonnaise evenly over 1 side of each bread slice.
Top 2 bread slices evenly with American cheese slices, tomato, avocado, and alfalfa sprouts.
Drizzle sandwiches evenly with reserved Italian dressing, and top with remaining 2 bread slices.
Serve immediately.