In a large non-stick skillet, over medium-high heat, warm 1 naan 1 minute per side. Repeat with remaining naan. Top each with arugula.
In a medium bowl, whisk eggs. Reduce heat to medium-low. In same skillet used for naan, heat oil. Pour in eggs. As eggs begin to set, move spatula across bottom and side of skillet to form large, soft curds. Cook just until no visible liquid egg remains.
Spoon egg mixture on top of arugula. Sprinkle each serving with oregano, salt and pepper. Top each with tomatoes, cucumber, onion (if using) and a dollop of tzatziki.
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