Squeeze excess liquid from crab. Place in bowl. Stir in mayonnaise, Monterey Jack cheese, goat cheese, chilies and cilantro. Arrange 5 tortillas on counter. Spread crab filling over each tortilla, leaving a border of about 1/2 inch. Brush border with egg white. Place another tortilla on top of the filling and press edges together gently but firmly. Heat about 1" oil in large non-stick skillet. Cook quesadillas one at a time for about 3 minutes per side, until browned. Cut each quesadilla into 6 wedges and serve with salsa. These can be made ahead of time and reheated in a 400 degree oven.
Cilantro Salsa: * from the Foley Fish Cookbook
Combine cilantro with sour cream, lime juice and Tabasco. (For lighter preparation: bake quesadillas in a preheated 400 degree oven for 15 minutes or cook in a non-stick pan lightly brushed with clarified butter or olive oil)