Prep: Preheat the oven to 350°F. Line a square 8x8-inch baking pan with parchment paper, leaving an overhang on two sides for easy removal.
Brown the butter: Cut 1/2 cup of the butter into cubes and place in a medium saucepan over medium heat. Cook, stirring frequently, until browned. The butter will foam and bubble as the water cooks off, then the milk solids will turn golden brown and the butter will smell nutty. Immediately remove the pan from the heat and stir in the remaining 1 tablespoon of butter until melted. Let cool until warm but not hot before adding the eggs.
1/2 cup unsalted butter, 1 Tablespoon unsalted butter
Mix the dry ingredients: While the butter is cooling, whisk together the flour, cinnamon, salt, and baking powder in a large bowl.
1 cup all-purpose flour, 1 teaspoon ground cinnamon, 1/2 teaspoon kosher salt, 1/2 teaspoon baking powder
Mix the wet ingredients: Add the brown sugar, granulated sugar, egg, egg yolk, and vanilla bean paste to the cooled butter and whisk until thick and smooth.
3/4 cup light brown sugar, 1/4 cup granulated sugar, 1 large egg, 1 egg yolk, 1 Tablespoon vanilla bean paste
Combine: Pour the wet ingredients into the dry ingredients and fold until just combined. Fold in the apples until evenly distributed.
3/4 cup Honeycrisp apples
Bake: Spread the batter into the prepared baking pan. Bake for 28 to 30 minutes, until the edges are set and a toothpick inserted into the center comes out with a few moist crumbs. Let cool completely before frosting.
Make the frosting: Beat the cream cheese and butter with a hand mixer or stand mixer for 1 to 2 minutes, until smooth and no lumps remain. Add the powdered sugar, vanilla bean paste, cinnamon, and salt and beat until fluffy, scraping down the bowl as needed.
4 oz full-fat cream cheese, 4 Tablespoons unsalted butter, 1 cup powdered sugar, 1 teaspoon vanilla bean paste, 1/2 teaspoon ground cinnamon, Pinch of salt
Frost and serve: Spread the frosting over the cooled blondies in thick swoops. Lift the blondies out of the pan using the parchment overhang. Cut into squares and serve.