In a mixing bowl, whisk together the flour, baking soda, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, combine the softened butter, light brown sugar, and granulated sugar. Mix until well combined, about 2 minutes. Add the eggs one at a time, mixing after each addition. Mix in the vanilla.
With the mixer running, slowly add the flour mixture and mix until just combined. Stir in the butterscotch chips and caramel bits.
Using a tablespoon cookie scoop, portion the dough onto a parchment-lined baking sheet. Put the sheet pan in the refrigerator and chill for one hour, or overnight.
Preheat the oven to 350 degrees. Bake the chilled balls of cookie dough for 10-11 minutes until lightly brown around the edges. Immediately after removing from the oven, press a few butterscotch chips and white chocolate chips into the top of each cookie. Sprinkle with flaked sea salt. Let cool on the baking sheet for 2-3 minutes before transferring to a cooling rack.
Store in an airtight container. The cookies will stay fresh for 3-4 days.