In a medium bowl, whisk together the softened cream cheese, powdered sugar, and vanilla extract until the mixture is smooth and uniform.
Spread an even layer of the cream cheese mixture onto one side of each of the eight flour tortillas.
Arrange the sliced strawberries in a single layer over the cream cheese on four of the tortillas.
Place the remaining four tortillas on top of the strawberry-layered tortillas, cream cheese side down, to form a sandwich.
Heat a large non-stick skillet over medium heat and melt 1 tablespoon of butter.
Place one or two quesadillas in the skillet and cook for 2 to 3 minutes per side until the tortillas are golden brown and the filling is warm.
While the quesadillas cook, combine the granulated sugar and cinnamon in a small bowl.
Remove the toasted quesadillas from the heat and immediately sprinkle the tops with the cinnamon-sugar mixture.
Slice each quesadilla into quarters and serve immediately.