Melt butter in a light-colored saucepan over medium heat, stirring continuously until it turns golden brown with fragrant bits (5-8 minutes), then immediately pour into a heatproof bowl and cool for 10-15 minutes.

Preheat your oven to 350°F (175°C) and line a 9x13 inch baking pan with parchment paper, ensuring an overhang for easy removal.

Add brown sugar and granulated sugar to the cooled brown butter, mixing well with a whisk; then incorporate eggs one at a time, mixing after each, and stir in vanilla extract.

In a separate medium bowl, whisk together the all-purpose flour, baking powder, salt, and the optional ground cinnamon.

Gradually add the dry ingredients to the wet ingredients, mixing only until no streaks of flour remain without overmixing, then gently fold in the chopped apples.

Spread the batter evenly into the prepared pan and bake for 25-30 minutes, or until the edges are golden brown and a toothpick inserted into the center comes out with moist crumbs.

Allow the blondies to cool completely in the pan on a wire rack before attempting to glaze.

In a small bowl, whisk together powdered sugar, 2 tablespoons of milk, and ¼ teaspoon of vanilla extract until smooth, adding more milk or powdered sugar as needed for desired consistency.

Once the blondies are entirely cool, pour the glaze evenly over the top and spread it; let the glaze set for at least 30 minutes before slicing and serving.