Make the blondies: Preheat the oven to 350˚. Line a 9-by-13-inch baking dish with foil, leaving a 2-inch overhang on two sides; coat the foil with cooking spray. Spread the walnuts on a baking sheet and bake until lightly browned, 10 to 12 minutes. Let cool slightly, then transfer to a cutting board and roughly chop; set aside.
Whisk the flour, baking soda and salt in a large bowl. Melt the butter in a medium saucepan over medium heat and cook, stirring occasionally with a whisk, until brown flecks appear, 10 to 12 minutes; remove from the heat and immediately whisk in the brown sugar and maple syrup. Let cool slightly, about 5 minutes. Whisk in the eggs one at a time, then add the vanilla and maple extracts.
Whisk the brown butter–egg mixture into the flour mixture, then fold in the walnuts with a rubber spatula. Spread the batter in the prepared pan. Bake until lightly browned and a toothpick inserted into the center comes out clean, about 25 minutes. Transfer to a rack and let cool completely in the pan. Lift the blondies out of the pan using the foil overhang; discard the foil.
Meanwhile, make the frosting: Beat the butter and salt in a large bowl with a mixer on medium-high speed until fluffy, about 2 minutes. Add the maple syrup and beat until smooth. Gradually beat in the confectioners' sugar on low speed, increasing the speed to medium high after each addition until fluffy. Beat in the lemon juice and maple extract; add more maple extract, 1/4 teaspoon at a time, to taste. Spread the frosting over the cooled blondies. Cut into squares.