Preheat the oven to 350°F. Line an 8x8 metal baking pan with parchment paper, leaving a little overhang on the sides for easy removal.
Add the butter to a saucepan over medium heat. Stir continuously as it melts and begins to foam. Keep cooking until the butter turns golden brown and gives off a nutty aroma. Watch closely, once browned, immediately pour it into a heat safe bowl to stop the cooking process. Make sure to get the brown bits off the bottom. Let it cool for at least 10 minutes before using.
In a large mixing bowl, whisk together the cooled browned butter, brown sugar, and granulated sugar until well combined. Add the egg, egg yolk, and vanilla extract, whisking until combined.
In a separate bowl, whisk together the flour, salt, baking powder, cinnamon, and nutmeg.
Add the dry ingredients to the butter mixture. Stir with a spatula until just combined.
Gently fold in the diced apples until evenly distributed throughout the batter, it will be thick.
Spread the batter evenly into the prepared pan, smoothing the top. Bake for 20–24 minutes or until the top looks set and golden brown. Do not overbake, they will continue to bake as they cool. Over baking will make them cakey instead of fudgy.
Let the blondies cool in the pan for about 15 minutes, then lift them out using the parchment paper and cool fully on a wire rack before icing.