Puree strawberries in a blender until smooth. Strain through a wire-mesh strainer into a small saucepan, pressing the pureed strawberries with a spoon until as much juice as possible has been squeezed out. Discard pulp.
Stir in sugar. Whisk together lemon juice and cornstarch. Gradually add the lemon juice mixture into the strawberry mixture. Over medium heat, bring to a boil and cook for at least one minute, stirring constantly. The mixture should become darker pink and begin to stick to the spoon when it is ready. Remove from heat. Chill in an airtight container for 2 hours.
Mix 3 tablespoons of strawberry lemonade preserves with minced Vidalia, olive oil and mustard.
Assemble sandwiches with an ample layer of strawberry-Vidalia on one slice of bread. Then add sliced cheese, turkey and another layer of cheese. Spread butter on one side of sandwich and flip it onto a pan warmed over medium heat. Then butter top of sandwich.