Toast the bagel: Split your bagel and toast until golden and crisp around the edges.
Prep the avocado: In a small bowl, mash the avocado with lemon juice, a pinch of salt, and black pepper. Keep some chunks for texture if you like.
Cook the egg: Heat butter or oil in a nonstick skillet over medium heat.
Fry the egg to your preference (sunny-side up, over easy, or over medium). For scrambled, whisk eggs with a pinch of salt and cook gently until soft and creamy.
Add cheese (optional): If using, place cheese on the egg during the last 30 seconds to melt.
Assemble: Spread the mashed avocado on both bagel halves. Add red pepper flakes or a dash of hot sauce if you like heat.
Layer it up: Set the egg on the bottom half, then add greens and tomato or pickled onions if using.
Top with the other half of the bagel.
Season and serve: Finish with a pinch more salt and pepper. Press gently, slice in half if you like, and enjoy right away.