Preheat the oven to 350°. Prepare and line an 8-inch square baking dish with grease and parchment. Set to the side.
Brown the butter. In a small saucepan on medium-low heat, melt the butter. The butter should foam, turn clear, and then brown. Make sure to continuously stir the butter while it is melting. The process should take 5-6 minutes depending on the heat. Make sure to watch the butter towards the end as it can burn very quickly. The butter is done when there is a nutty aroma to it. Once butter is browned, take off the heat and pour into a heatproof bowl. Let it cool while you prepare the batter.
In a medium-sized bowl, combine the brown sugar, egg, vanilla, and salt. Whisk to combine. Add the butter once it has cooled down. Fold in the flours, followed by 1 cup of the cherries and almost all of the white chocolate chips. Leave a few out to throw on top.
Using a spatula, add the blondie batter to the pan. The dough will be very sticky, don't worry. You can use a spatula to pat it down flat or some parchment paper to flatten it down. Once the batter is flat, add the remaining cherries and white chocolate chips on top.
Bake for 35-45 minutes. The blondies will be done when they are not gooey in the middle.
Let the blondies cool completely before cutting. Store in an airtight container in the refrigerator. The blondies should last about a week if using fresh cherries.