In a small skillet saute onion in butter over medium heat until translucent. Cool.
Place scallops in food processor and pulse until coarsely chopped or chop by hand. Transfer to large bowl and add remaining ingredients, except vegetable oil. Add in the cooled onions.*
Shape the mixture into small burgers, approximately 2 inches in diameter. Place on a waxed paper lined sheet tray, cover with plastic wrap and chill for at least 1 hour.
Heat 2 tablespoons vegetable oil in a skillet over medium heat. Add scallop sliders and cook until browned and cooked through. Place on small soft dinner rolls and top with a bit of Cilantro-Lime Mayo. Serve warm or at room temperature.
Blend all ingredients in food processor except mayonnaise and salt and pepper. Process until cilantro is fine. Add mayonnaise and process just until blended. Season with salt and pepper, to taste
*Mixture should not be too loose. If necessary, add a bit more flour or another egg. Cilantro-lime mayo is good with any seafood or fish, especially salmon.