Chop the basil, parsley, and shallot finely and mince the garlic.
In a bowl, combine the mayonnaise, chopped herbs, shallot, minced garlic, Dijon mustard, and lime juice and stir until smooth; refrigerate for up to 1 hour if desired to let flavors meld.
Toast the bread slices in a toaster or in a skillet over medium heat if you like your sandwich toasted.
Spread the herb mayo evenly on each slice of bread.
Layer leftover chicken, tomato slices, avocado slices, and arugula on two slices of the prepared bread.
Top with the remaining bread slices, cut each sandwich in half diagonally, and serve.