Melt butter in a light-colored skillet over medium heat, stirring constantly until milk solids turn chestnut brown and emit a nutty aroma, then cool to room temperature.
Combine the browned butter and sugars in a stand mixer bowl and cream on medium speed for 2-3 minutes until the mixture is light and fluffy.
Incorporate eggs one at a time, followed by the vanilla extract, ensuring each addition is fully emulsified before proceeding.
Whisk together flour, baking soda, and kosher salt in a separate container to ensure even distribution of leavening agents.
Add the dry ingredients to the wet mixture on low speed, mixing until just combined to avoid gluten over-development.
Fold in the butterscotch chips and chocolate chips manually using a spatula.
Refrigerate the dough for at least 30 minutes to hydrate the flour and minimize spread during baking.
Preheat oven to 350°F (175°C) and line baking sheets with parchment paper.
Portion the dough into 40g spheres and arrange on sheets 5cm apart.
Bake for 10-12 minutes until the periphery is golden brown and the center remains soft to the touch.
Remove from heat and immediately apply a pinch of flaky sea salt to each cookie before cooling on the sheet for 5 minutes.