Some restaurants are able to make Monte Cristo's that are not greasy at all. But some do make them a bit greasy. If you're curious, here is a recipe that claims to be an imitation of the Blue Bayou's version:
BLUE BAYOU MONTE CRISTO SANDWICH
BATTER:
1 1/2 c. all-purpose flour
1/4 tsp. salt
1 tbsp. baking powder
1 1/2 c. water
1 egg
SANDWICH:
1 oz. sliced white turkey
1 oz. sliced Swiss cheese
1 oz. sliced ham
2 slices white bread
2 tsp. jelly
To make batter sift flour, salt and baking powder together. Add water to beaten egg and then to flour mixture. Mix well and then set aside.
To make sandwich use 1 slice of turkey, Swiss cheese and ham on 2 pieces of white bread. Then cut into quarters using toothpicks to hold sandwich together. Dip sandwiches in egg batter completely and deep fry at 360 degree oil until golden brown. Remove toothpicks and sprinkle with powdered sugar. Serve with your favorite jelly and fruit cocktail.