Traditionalists may grumble, but we think topping St. Louis-style gooey butter bars with fresh berries is a stroke of midsummer genius.
Preheat oven to 350°F. Line a 13x9x2-inch baking pan with parchment paper, extending the paper over edges of pan; set aside.
For crust, in a medium bowl stir together 1 1/2 cups flour and 1/4 cup sugar. Using a pastry blender, cut in 1/2 cup butter until mixture resembles fine crumbs (mixture will be dry and crumbly). Press into the bottom of the prepared baking pan.
In a large mixing bowl, beat 2/3 cup butter with an electric mixer on medium to high speed for 30 seconds. Gradually beat in 1 1/4 cups sugar. Beat in egg, corn syrup, and almond extract just until combined. Alternately add 1 cup flour and the half-and-half to egg mixture, beating on low speed after each addition just until combined (batter may appear slightly curdled). Spread batter over crust.
Bake about 30 minutes or just until center is set. Cool in pan on a wire rack. Using the edges of the parchment paper, lift uncut bars out of pan. Cut into bars.
In a small bowl combine strawberries, honey, and ginger; toss gently to coat. Spoon over bars before serving.