Place eggs in a saucepan and cover with water. Bring to a boil, remove from heat, cover, and let eggs stand in hot water for 10 to 12 minutes. Remove eggs from hot water, cool under cold running water, and peel.

Combine mayonnaise, green onions, lemon juice, Dijon mustard, and yellow mustard in a large bowl until well combined.

Chop eggs into big chunks; add to the bowl with dressing. Gently stir until evenly combined; season with salt and black pepper.