Melt butter in a light-colored skillet over medium heat. Swirl frequently. When foam subsides and brown specks form, remove from heat.

Transfer to a cool bowl immediately to stop cooking. The butter should smell nutty, not burnt.

Combine brown butter with brown sugar and granulated sugar; beat until glossy. Add eggs one at a time, then vanilla.

Whisk flour, baking soda, and fine sea salt in a separate bowl. Fold into wet ingredients just until combined; avoid overmixing.

If using wrapped squares, unwrap them and set on parchment. For homemade caramel, chill spoonfuls so they’re firm enough to drop into dough.

Scoop ~2 tbsp of dough, flatten slightly, place a caramel piece in the center, and fold dough around it to seal. Roll into a ball and chill on a baking sheet for 30–45 minutes.

If a caramel peeks out, pinch the dough closed; a small seam is okay — the cookie will still be delicious.

Preheat oven to 350°F (175°C). Place cookies 2 inches apart on a lined baking sheet. Bake 10–12 minutes until edges are set but centers are soft.

Immediately sprinkle with coarse sea salt when they come out of the oven.

Let cookies cool 10 minutes on the baking sheet — the caramel will set slightly but remain gooey. Transfer to a rack to cool completely.