Step 1: In a small bowl, whisk the white miso paste into the caramel sauce until completely smooth and set aside.
Step 2: In a large mixing bowl or stand mixer, cream together the cooled browned butter, brown sugar, and granulated sugar until light and fluffy.
Step 3: Add the egg and vanilla extract, beating until well combined.
Step 4: Stir in the miso-caramel mixture until the dough is a uniform amber color.
Step 5: In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Step 6: Cover the dough and refrigerate for at least 2 hours (ideally overnight).
Step 7: Preheat your oven to 350°F (175°C) and line baking sheets with parchment paper.
Step 8: Scoop rounded tablespoons of dough onto the sheets, spaced 2 inches apart.
Step 9: Bake for 10-12 minutes until the edges are golden brown but the centers still look slightly soft.
Step 10: Allow the cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack.