Pickled red onions: Mixed the water, vinegar, sugar, and salt until combined, then add red onion slices. Cover and let sit for 1 hour. Mayo aioli: Combine the mayo, vinegar, and garlic in a bowl and mix well. Both can be made ahead and keeps for 2 weeks.
Make your sandwich to your liking–add as much or little of arugula, avocado, and red onions. Lightly toast your bread and fry up the egg (over-easy) at the same time. Coat toasted bread with mayo aioli, then top with arugula, avocado slices (slightly overlapping), the fried egg, and lastly the red onions. Enjoy!