Heat the oil in a medium skillet set over medium heat. Once oil is hot and shimmers, add the onion and cook for 2 to 3 minutes, until wilted but not browned. Incorporate the chaya and mint, mix, and continue cooking for a couple minutes, until completely cooked and wilted.
Meanwhile, in a small bowl, beat the eggs and season with the salt and pepper.
Reduce heat to medium low, pour the eggs over the onion and chaya mixture and, as they cook, scramble with a wooden spoon or spatula. Cook until desired doneness. I like my eggs tender, so I cook them for 2 to 3 minutes.
Serve with warm corn tortillas, habanero table salsa, ripe avocado slices, and colado black beans or refried beans.