Preheat oven to 350°F. Line 13x9-inch baking pan with parchment paper and set aside.
Crust: Whisk together flour and sugar. Using a pastry blender (or two forks), cut butter into dry ingredients until mixture resembles coarse crumbly sand. Transfer into prepared pan and press into an even layer. Set aside.
Filling: In the bowl of a stand mixer fitted with a paddle attachment (or using an electric hand mixer), beat butter and sugar until smooth. Scrape sides of bowl as needed.
Add corn syrup, egg, and vanilla extract. Continue to mix until well combined.
Add flour in three additions, alternating with milk. Mix until just combined. Transfer batter into prepared pan over crust.
Bake for 28-30 minutes until the center of the cake no longer jiggles. Cool to room temperature in pan. Cake will harden as it cools. Remove from pan and slice into bars.
Topping: In a small bowl, toss together strawberries, grapefruit, honey, and ginger. Garnish tops of cooled butter bars with fruit.