Preheat the oven to 400° Whisk the oil with the vinegar, salt and pepper. Toss half the mixture with the mushrooms and brush the remaining over all over the chicken. Arrange the mushrooms and chicken on a parchment-lined baking sheet. Bake for 20 minutes or until cooked though; cool slightly. Chop the chicken into pieces. Toss the chicken and mushrooms with the asparagus, 1/2 cup marinara sauce, sun dried tomatoes and olives (if using). Sprinkle half the cheese on one side of each tortilla. Divide the chicken mixture evenly over the cheese and top with remaining cheese. Fold the tortillas over to enclose the filling. Set a large, nonstick skillet over medium heat and coat with cooking spray. Place 2 quesadillas in the skillet and cook for 2 to 3 minutes per side or until lightly toasted and cheese is melted. Repeat with remaining quesadillas. Serve with the remaining marinara sauce and sour cream for dipping.
Lightly brush the outside of the quesadillas with olive oil and cook on an outdoor grill preheated to medium. The chicken and mushrooms can be grilled, if preferred. Make the filling up to 1 day ahead and prepare the quesadilla just before serving.