Combine first 7 ingredients in a medium bowl; stir well. Remove rind from cheese; cut cheese into thin slices, and arrange slices evenly on 5 tortillas. Spoon crabmeat mixture evenly over cheese, and top with remaining tortillas.
Coat a large nonstick skillet with cooking spray; place over medium-high heat until hot. Add quesadillas, one at a time, and cook 1 to 2 minutes on each side or until lightly browned and cheese melts. Cut each quesadilla into 4 wedges, and serve immediately.