Place shrimp in a food processor and purée roughly. Add eggs, salt, and pepper, and continue processing until purée is fairly smooth.

Spoon shrimp purée into a bowl and fold in cheese. Mix until all ingredients are combined. Reserve.

Using a 1½-inch cookie cutter, cut tortillas into small rounds.

Place half of the tortilla rounds on a board or platter and spoon 1 tablespoon of shrimp mixture on each of the tortillas. Top with remaining tortilla rounds. (You now have small tortilla sandwiches.) Place quesadillas in refrigerator and chill for 30 minutes.

Lightly oil a griddle or sauté pan, preferably with a nonstick surface. Cook quesadillas over low heat, turning until they’re crisp and golden on both sides.

Using a slotted spatula, remove quesadillas from griddle or pan and drain on paper towels.