Cut butter into chunks and place in a small saucepan over low heat. Stir butter with a wooden spoon until it is melted.
Once the butter is melted, continue to cook over low heat, swirling the pan occasionally, until small brown specks appear and the butter emits a nutty aroma. Immediately pour butter into a glass dish, making sure to scrape all the brown specks from the pan into the dish.
Allow the butter to cool slightly, and then place the glass bowl into the refrigerator for approximately 2 hours or until the butter is solid but still a bit soft.
In a medium bowl, sift together flour, baking powder, and baking soda. Set aside.
Cream together brown butter, granulated sugar, and light brown sugar using a stand or handheld mixer.
Add in eggs, vanilla, milk, and salt, and continue mixing to combine.
With your mixer on low speed, slowly add in the dry ingredients and stir until just combined. Finally, add the chocolate chips and toffee chips and mix until well distributed.
Remove the dough from the bowl and wrap in plastic wrap. Refrigerate for 30 minutes to 1 hour.
Preheat the oven to 375°F, and line baking sheets with parchment paper.
Remove dough from the refrigerator, and form balls of 4 tablespoons of dough. Press each ball down slightly, and arrange them about 3 inches apart on baking sheet.
Bake for 9-12 minutes until edges are golden brown. Sprinkle them with sea salt. Let the cookies cool for 10-15 minutes on the baking sheet and then transfer them to a wire cooling rack. Enjoy!