Preheat oven to 350 degrees F.
In a small saucepan, combine strawberries, 1/4 cup sugar and lime juice. Cook over medium heat until mixture reduces to 1/2 cup. Remove from heat.
In a small bowl, combine 3/4 cup sifted flour, graham cracker crumbs, baking powder and salt. Whisk ingredients together and set aside. In a medium bowl, combine butter with brown sugar and mix well. Add 1 egg, cinnamon, ginger and vanilla. Blend well. Add flour mixture, a little at a time, mixing well. Spread in a buttered 8x8x2-inch square pan.
In same medium bowl, combine cream cheese, 2 tablespoons flour and the remaining egg. Alternately spoon cream cheese mixture and cooked strawberries onto blondie layer. Using a knife, swirl to marble.
Bake at 350 degrees F. for 40 – 50 minutes or until center is set. Remove pan from the oven and place on a wire rack to cool for 30 minutes. Cut the blondies into 2-inch squares. Refrigerate leftovers (although there won’t be any!).
Makes 16 (2-inch) squares