Preheat oven to 350 degrees. Butter a 9-by-13-inch baking pan. Line bottom of pan with parchment paper; butter and flour parchment paper.
In a saucepan over medium heat, cook the butter until it turns golden brown; remove from heat, and let cool. Whisk together flour, baking powder, and salt.
In the bowl of an electric mixer, combine browned butter and both sugars; stir with a wooden spoon until combined. Attach bowl to mixer; add eggs. Using the paddle attachment, beat on medium-high speed until light and fluffy, about 3 minutes. Add vanilla, and beat to combine. Add flour mixture, walnuts, and toffee bits. Mix until thoroughly combined, and pour into prepared pan.
Bake until a cake tester inserted in the center comes out clean, 35 to 40 minutes (do not overbake). Transfer to a wire rack to cool completely before turning out of pan onto a cutting board. Peel off parchment paper; cut blondies into 3-inch squares. Blondies can be stored in an airtight container at room temperature up to 3 days.