Brown the Butter: Melt butter in a stainless steel pan over medium heat, stirring constantly until golden and nutty. Pour into a bowl and cool 20–30 minutes.
Mix Wet Ingredients: Combine cooled butter, brown sugar, and granulated sugar. Stir until smooth, then add egg, milk, and vanilla.
Combine Dry Ingredients: Whisk flour, baking soda, and salt in a bowl, then fold into wet ingredients.
Add Chocolate: Stir in dark chocolate chunks and semisweet chips.
Chill Dough: Cover and refrigerate for 1–4 hours for thicker cookies.
Bake: Preheat oven to 375°F (190°C). Scoop 2 oz dough balls onto parchment-lined sheets. Bake 8–10 minutes until golden edges and soft centers.
Cool and Serve: Cool on pan 2 minutes, transfer to rack, sprinkle with flaky sea salt, and enjoy!
