Place 1 cup unsalted butter in a light-colored saucepan or skillet over medium heat. Melt the butter, swirling the pan occasionally, until it foams and turns a golden amber color with brown specks at the bottom, which should take about 5 to 7 minutes. Immediately pour the brown butter into a large heatproof bowl to stop the cooking and let it cool for 15 minutes.
Preheat your oven to 375°F and line two large baking sheets with parchment paper.
Add 1 cup packed light brown sugar and 1/2 cup granulated sugar to the cooled brown butter. Using an electric mixer, beat on medium speed for 2 minutes until well combined. Beat in 2 large eggs and 1 1/2 teaspoons vanilla extract until the mixture is smooth and creamy.
In a separate bowl, whisk together 2 1/2 cups all-purpose flour, 1 teaspoon baking soda, and 1 teaspoon kosher salt. Gradually add the dry ingredients to the wet ingredients, mixing on low speed just until no flour streaks remain. Fold in 1 1/2 cups semi-sweet chocolate chips and 1/2 cup soft caramel bits with a spatula until evenly distributed.
Scoop heaping 2-tablespoon portions of dough and place them 2 inches apart on the prepared baking sheets. Bake for 9 to 11 minutes, or until the edges are golden brown and the centers look slightly soft.
Remove the cookies from the oven and immediately sprinkle the tops with 1 teaspoon flaky sea salt. Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely, which will allow them to set properly.
