Preheat oven to 350°F (180°C). Spray a 9-inch square baking pan with cooking spray. Line pan with parchment paper, letting excess extend over sides of pan.
In a large bowl, whisk together brown sugar and melted butter until smooth and well combined; whisk in eggs and gingerbread vanilla extract.
In a medium bowl, whisk together flour, baking powder, salt, ginger, cinnamon, nutmeg, and cloves. Stir flour mixture into butter mixture just until dry ingredients are moistened. Fold in white chocolate. Using an offset spatula, spread batter into prepared pan.
Bake until golden brown and a wooden pick inserted in center comes out with a few moist crumbs, 25 to 35 minutes. Let cool completely in pan on a wire rack.
Using excess parchment as handles, remove from pan. Cut into 3 (9x3-inch) strips. Cut each strip into 7 (2-inch-wide) triangles.
Transfer Vanilla Bean Buttercream to a pastry bag fitted with a small closed star piping tip (Ateco #842), and pipe onto blondies. Garish with sprinkles, if desired. Store in an airtight container for up to 3 days.