1. In a small saucepan over medium heat, cook butter, stirring often until foamy and beginning to brown.
2. Move the browned butter to a small bowl, scraping the saucepan, and allow to cool slightly.
3. In a medium bowl, whisk flour, baking soda, and kosher salt; set aside.
4. In the work bowl of a stand mixer, add brown sugar, granulated sugar, and browned butter.
5. Beat on medium speed until well incorporated.
6. Add eggs and vanilla; beat until mixture lightens and begins to thicken.
7. Turn speed to low, add flour mixture, and beat until just combined.
8. Add chopped toffee bars and chocolate chunks; stir with a wooden spoon or rubber spatula.
9. Prior to baking, allow dough to rest at room temperature for at least 30 minutes, until thickened.
10. Preheat oven to 350°F Convection Mode with racks set at positions “1,” “3,” and “5.”
11. Scoop 2-tablespoon portions of dough onto parchment-lined cookie sheets, spacing about 3 inches apart. Sprinkle with sea salt.
12. Bake until edges are golden brown and firm but centers remain soft, about 10 minutes.
13. Cool on baking sheets for 15 minutes, then transfer to a wire rack and cool completely.