In a small saucepan over medium heat, melt the unsalted butter for the caramel. Stir in light brown sugar and whisk continuously until the sugar dissolves and the mixture comes to a gentle boil.

Slowly whisk in heavy cream and keep whisking for 2–3 minutes until the sauce thickens enough to coat the back of a spoon. Remove from heat, stir in flaky sea salt, and let cool until warm.

In a medium bowl, whisk together all-purpose flour, cornstarch, baking soda, and fine sea salt until evenly distributed.

Using a handheld mixer, beat the softened unsalted butter with packed light brown sugar and granulated sugar on medium speed for about 3–4 minutes until pale and fluffy.

Add the room-temperature egg and vanilla extract to the butter-sugar mixture, mixing on low speed just until incorporated.

Gradually add the dry-ingredient mixture to the butter mixture, stirring on low speed until a cohesive dough forms.

Drizzle the warm caramel over the dough in streams and fold gently with a spatula until visible ribbons of caramel appear.

Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper. Using a cookie scoop, drop rounded mounds of dough onto the sheet, spacing them 2 inches apart. Bake for 12–14 minutes.

Immediately sprinkle flaky sea salt on warm cookies. Let rest for 5 minutes then transfer to a wire rack to cool completely.