Prepare the Salted Caramel: In a saucepan over medium heat, combine granulated sugar, stirring continuously until it melts and turns deep amber, about 10 minutes. Add unsalted butter and heavy cream, mixing until smooth. Remove from heat and stir in a pinch of flaky sea salt. Allow to cool.

Mix the Wet Ingredients: In a large mixing bowl, cream together softened butter, granulated sugar, and brown sugar until light and fluffy, about 3-5 minutes. Add egg and vanilla extract, mixing well.

Combine the Dry Ingredients: In a separate bowl, whisk together flour, baking soda, and salt until combined. Gradually add to wet ingredients, mixing on low speed until just combined.

Chill the Cookie Dough: Cover with plastic wrap and refrigerate for at least 30 minutes. Preheat oven to 350°F (175°C).

Form and Bake the Cookies: Line a baking sheet with parchment paper. Scoop out tablespoon-sized portions of dough, place 2 inches apart, and create an indentation in the center. Fill with salted caramel. Bake for 12 minutes.

Cool the Cookies: Remove from oven and let cool on the baking sheet for 5 minutes before transferring to a wire rack.