Cook the butter in a saucepan over medium heat, stirring frequently, until browned (5–8 minutes). Let cool for about 10 minutes.
Whisk flour, baking soda, and salt in a separate bowl.
Add sugars to the cooled butter and mix well. Beat in eggs and vanilla until light and thick. Combine with dry ingredients, then stir in toffee bars and chocolate wafers.
Let the dough sit for at least 30 minutes to thicken.
Preheat oven to 375°F and prepare a baking sheet. Scoop out dough onto the sheet, spacing them 3 inches apart. Sprinkle with sea salt.
Bake until edges are golden and centers are soft (9–11 minutes). Let cool on baking sheets for 10 minutes, then transfer to a wire rack to cool completely.
Dough can be prepared 3 days ahead; chill in the refrigerator or freeze for up to 3 months.
Notes
For best flavor, allow dough to rest and hydrate before baking.