In a medium saucepan, melt ½ cup salted butter, browned over medium heat. Stir constantly until the butter foams, then turns golden brown with a nutty aroma. Once browned, remove from heat and set aside to cool slightly.
In a mixing bowl, combine the brown butter, 1 tablespoon salted butter, ⅓ cup creamy peanut butter, ¾ cup brown sugar, and ¼ cup granulated sugar Use a hand mixer or stand mixer to beat until smooth and well incorporated.
Beat in the 1 large egg and 1 teaspoon vanilla extract, mixing until fully combined.
In a separate bowl, whisk together the 1¼ cups all-purpose flour, ½ teaspoon baking soda and ½ teaspoon salt. Gradually add the dry ingredients to the wet mixture, stirring until just combined.
Fold in the ¾ cup chocolate chips or chopped chocolate until evenly distributed.
Cover the dough and refrigerate it for at least 30 minutes to firm up the dough.
Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
Roll the dough into 1-inch balls and place them on the prepared baking sheet, leaving space between each cookie. Press them down lightly with a fork or your fingers to flatten slightly. Sprinkle with 1 teaspoon Flaked salt if desired.
Bake the cookies for 10-12 minutes or until the edges are golden brown. Remove from the oven and let them cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.