Preheat oven to 350° F.
Line a 9x9-inch baking pan with parchment paper, letting it hang over the sides. To keep the paper in place, attach a binder clip to each side.
Using an ice cream scoop, scoop the cookie dough into the lined baking dish. Using clean hands, press the dough into an even layer.
Bake for 25 to 30 minutes, or until just lightly blonde at the top and set in the center. Allow the blondies to cool completely.
While the blondies are baking, prepare the maple brown butter frosting. Add 1 stick of butter to a skillet over medium heat.
Allow the butter to melt evenly and completely, stirring with a rubber spatula or wooden spoon. Once the butter has melted, stir frequently and cook until the foam subsides slightly and the butter is golden with a toasted nutty aroma, about 4 to 5 minutes. (Note: You may notice brown specks in your butter. That's OK! These are toasted milk solids and will add loads of flavor to the frosting.)
Add the brown butter, remaining stick of butter, cream cheese, powdered sugar, maple syrup, and vanilla extract to a stand mixer with the whisk attachment. Beat on medium speed for 2 to 3 minutes, or until smooth and fluffy.
Top the cooled blondies with the maple brown butter frosting using a rubber spatula.
Slice into squares and enjoy!
