In the bowl of a stand mixer, cream butter and sugars together. Add vanilla and egg and mix. Add the rest of the ingredients, up to chocolate chips and mix until combined. Stir in chocolate chips and caramel bits by hand. Place dough in refrigerate and chill for 2 to 4 hours.
Pre-heat oven to 350F. Line baking sheets with parchment paper or a silpat.
Using a medium scoop, scoop the dough and place on baking sheet, about 2 inches apart. Take care that the caramel bits are not on the bottom of the cookies as they will caramelize. Bake for 12 to 14 minutes or until lightly browned at the edges. Sprinkle sea salt on top of cookies while still warm.
Cool cookies on the baking sheet on a wire rack for 5 to 10 minutes, then remove the cookies and finish cooling on the wire rack. If you’ve got a steady hand you can carefully transfer the silpat or parchment paper to the wire rack and cool that way.