Use a hand or stand mixer to mix together melted brown butter, brown sugar, and granulated sugar until it's smooth and creamy.
Add eggs, vanilla, and almond extract, and beat until the mixture is light and fluffy (around 3-5 minutes; it should look lighter in color).
Mix in flour, baking powder, and salt until everything is well combined. The dough should be wet and sticky.
Gently fold in dark chocolate chips using a spoon or spatula.
Cut a piece of parchment paper slightly smaller than the cake pan's width. Spray the pan with a vegetable oil spray, then place the parchment paper inside, securing it with metal binder clips if needed. This will make it easy to remove the brown butter blondies from the pan after baking.
Spoon the dough into the pan you prepared and press it down to make an even layer. You can use wet fingers to flatten it out easily. If you like, press some extra chocolate chips on top of the dough.
Put the pan in the fridge for 15-20 minutes to make the dough a bit firmer before baking.
While the blondies are chilling, heat the oven to 350°F.
Bake the blondies at 350°F for 30-35 minutes or until the top is golden brown and a toothpick inserted in the middle comes out mostly clean.
Take the pan out of the oven and let the blondies cool completely in the pan. Then, use the edges of the parchment paper to slide them out.
Cut into squares and sprinkle with flaky sea salt if you like!