Set up grill for direct cooking over medium heat and oil grate when ready to cook.
Lay out 4 tortillas; top each tortilla with brie, smoked turkey, apricot preserves, and Jack cheese. Top with remaining tortillas.
In a bowl, toss to combine herbs and lemon juice. Season with salt and pepper; set aside.
Place quesadillas on hot oiled grill for 3 to 4 minutes per side or until cheese has melted flipping with a spatula. Serve hot topped with mixed herb salad.
Prepare quesadillas as directed. In a skillet large enough to fit tortillas, heat 1 to 2 tablespoons of vegetable oil over medium heat. When oil is hot, carefully fry both sides of quesadillas for 2 to 3 minutes or until golden brown; turning with a large spatula. Garnish, as directed.