Preheat the oven to 350°F. Line baking sheets with parchment paper. Set aside.
In a stainless steel skillet (or other light-bottomed pan), melt the butter over medium-high heat. Swirl the pan occasionally as it begins to foam.
As soon as the butter turns chestnut brown and smells nutty, remove the pan from the heat. Pour the browned butter into a heat-safe bowl.
Stir in the brown sugar. Let the mixture cool for 15–20 minutes.
In a medium bowl, whisk together the flour, baking soda, salt, and baking powder. Set aside.
Once the butter mixture is slightly cooled but still fluid, whisk in the eggs and vanilla until smooth.
Using a rubber spatula, gradually stir in the dry ingredients until just combined. Do not overmix.
Fold in the chocolate and butterscotch chips. The dough will be soft.
Scoop dough into 3-tablespoon-sized portions and place on the prepared baking sheets, leaving 1–2 inches between each.
Bake for 12–14 minutes, or until golden brown and just set around the edges. (For a softer center, start checking around 10 minutes.)
Remove from the oven and immediately sprinkle with salt.
Let cookies cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.