In a medium bowl, gently whisk the eggs with the salt and pepper until just combined. You want a smooth mixture, not too foamy.
Heat an 8-inch non-stick skillet over medium-low heat. Add about 1/4 teaspoon of butter or oil and swirl to coat the pan.
Pour about 1/4 cup of the egg mixture into the hot skillet. Tilt the pan to spread the egg evenly into a thin circle, similar to a crepe.
Cook for 1 to 2 minutes, or until the edges are set and the center is mostly firm. Gently loosen the edges with a spatula, then carefully flip the egg wrap and cook for another 30 seconds to a minute until lightly set.
Slide the cooked egg wrap onto a plate and repeat the process with the remaining egg mixture, adding more butter or oil as needed, until you have 4 wraps.
To assemble each wrap: Spread 1 tablespoon of avocado oil mayonnaise evenly over one side of an egg wrap. Layer with 4 slices of deli turkey, 2 slices of crispy bacon, a few tomato slices, and a handful of fresh lettuce leaves.
Carefully roll up the wrap tightly. You can slice it in half for easier eating if desired. Serve immediately and enjoy your healthy, satisfying meal!