Preheat your oven to 350°F and line two baking sheets with parchment paper.
In a large bowl, beat together the butter, brown sugar, and granulated sugar until creamy and smooth, about 2-3 minutes.
Add the egg and vanilla extract, beating until well incorporated.
In a separate bowl, whisk together the flour, baking soda, and salt. Gradually stir the dry ingredients into the wet ingredients until just combined.
Fold in caramel chips until evenly distributed.
Scoop rounded tablespoons of dough and roll into balls. Place them about 2 inches apart on your prepared baking sheets.
Bake for 9-11 minutes until edges are golden and centers look slightly underdone; they will keep cooking on the sheet.
Immediately sprinkle each hot cookie with a small pinch of flaky sea salt.
Cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.