Toss the pears with the brown sugar in a small bowl. Heat the butter in a medium skillet over medium-high heat. Add the pears in a single layer and cook until golden brown, about 2 minutes on each side. Transfer to a plate and let it cool.

To make the quesadilla: On a work surface, spread 2 of the tortillas. Sprinkle the gorgonzola cheese over the bottom of each tortilla. Add the pears evenly on top of the cheese, then top with pecans. Top with another tortilla.

Heat a large nonstick skillet with cooking spray over medium heat. Carefully place 1 quesadilla in pan and cook 2 minutes. Using a spatula, gently flip the quesadilla and cook an additional 2 minutes until lightly browned and cheese is melted. Repeat with second quesadilla. Serve warm over arugula drizzled with balsamic vinegar.