Preheat oven to 350 degrees F. Line a 13x9x2-inch baking pan with foil, extending the foil over edges of pan. Grease foil; set pan aside.
In a medium saucepan cook and stir brown sugar, the 2/3 cup butter, and the 1/2 cup maple syrup over medium heat until butter is melted and mixture is smooth. Remove from heat; cool slightly. Stir in eggs and vanilla. Stir in flour, baking powder, and baking soda until combined. Gently stir in raspberries.
Pour batter into the prepared baking pan, spreading evenly. Bake for 25 to 30 minutes or until a wooden toothpick inserted near the center comes out clean. Cool in pan on a wire rack.
For frosting, in a medium bowl stir together powdered sugar, the 1/4 cup maple syrup, the 2 tablespoons softened butter, and the milk until smooth. Spread frosting on cooled bars. Spoon raspberry preserves in small mounds on top of frosting. Using a narrow metal spatula or a table knife, swirl slightly to marble. Using the edges of the foil, lift uncut bars from pan. Cut into bars.