Prepare the Pan: Adjust the oven rack to the middle position and preheat to 350°F. Line a 9x13-inch baking pan with foil, ensuring the bottom and sides are covered, and lightly grease. Sift the flour into a medium bowl and set aside.
Make the Brown Butter: In a 2-quart saucepan, melt the butter over medium-low heat. Increase heat to medium and stir constantly as the butter bubbles and browns. Once golden yellow with a nutty aroma, remove from heat and stir in white chocolate until melted. Set aside to cool slightly.
Mix the Batter: In a stand mixer bowl, combine brown sugar, granulated sugar, malted milk powder, salt, eggs, and vanilla. Whip on medium-high speed until light and fluffy, about 8 minutes. Reduce the speed to low and mix in the butter mixture. Add the flour and fold until fully incorporated.
Bake the Blondies: Pour the batter into the prepared pan and smooth the surface. Bake for about 35 minutes, or until the edges are set, the top is glossy, and the center registers 210°F. Cool completely at room temperature before cutting.
Cut and Store: Use the foil overhang to lift the blondies from the pan. Slice into 24 squares. Store in an airtight container with wax paper between layers for up to 1 week at room temperature.