Heat the olive oil in a 9-inch skillet over medium high heat. Add the sliced onion and fry, stirring frequently, until softened and caramelized (about 10 minutes). Transfer the cooked onions to a plate.
Wipe out the skillet with a dry paper towel. Return the skillet to medium heat. Add the first tortilla. Spread the cooked onions evenly over the tortilla. Top with the brie slices and then the pear slices. Place the second tortilla on top. Push gently down to flatten the quesadilla and leave to heat for about 5 minutes. Take care not to over heat/cook the bottom tortilla. You want to warm through the ingredients, not cook them. Turn the heat down if necessary.
After about five minutes, turn the tortilla over (I like to slide the tortilla onto a plate and invert back into the skillet. This is tricky to flip.). Leave to warm through for another 5 minutes, or until the brie has melted and is oozing on the sides.
Transfer to a chopping board and cut into small wedges if serving as an appetizer. Enjoy while warm.
If you are short on time, you can substitute an onion jam for the caramelized red onions. I have made it like this and it is also delicious.