Heat a medium non-stick skillet over medium heat. Add a pat of butter or drizzle of oil and let it melt.
Crack eggs into the pan. Whisk lightly with a fork right in the pan until scrambled. Season with salt and pepper. Let cook 1 minute until edges set.
Place both slices of bread on top of the eggs. Press down gently. Add cheese slice on one bread piece.
Layer avocado, tomatoes, and lettuce on the cheese-topped bread.
Carefully slide spatula under the eggs and bread. Flip one bread slice over the other to close the sandwich. Fold any overhanging egg inward.
Press down with spatula and cook 2 minutes per side until bread is golden and crispy, cheese melts.
Slide onto plate. Cut in half and dig in hot.