In small nonreactive saucepan (one made from material that does not react with acidic ingredients), bring balsamic vingar, honey, and lemon juice to a boil reduce heat to medium and simmer uncovered until syrupy and reduced to 1/4 cup about 10 mintues. Set aside to cool.
Heat skillet over medium heat Meanwhile divide spinach, goat cheese, strawberries, mint, and walnuts over half of each tortilla, leaving a 1/2 inch border. Drizzle balsamic syrup over top and then fold over tortillas to enclose toppings.
In warmed skillet, heat quesadilas for 1 1/2 minutes, or until bottom of tortillas are darkend and crispy. Carefully flip and cook for 1 1/2 minutes more. Slice in half to serve.
