Preheat oven to 350 degrees F. Line a baking sheet with parchment paper or a silicone baking mat; set aside.
Melt butter in a medium saucepan over medium heat. Cook, whisking constantly, until the foam subsides and the butter begins to turn a golden brown, about 3 minutes. Remove from heat.
In a medium bowl, combine flour, baking soda and salt.
In the bowl of an electric mixer fitted with the paddle attachment, beat browned butter and sugars on medium-high until well combined, about 1-2 minutes. Beat in vanilla and eggs, one at a time, until well combined. Gradually add flour mixture to sugar mixture at low speed, beating just until incorporated.
Gently fold in toffee bits, chocolate chips and Rolos.
Drop tablespoons of batter onto prepared baking sheet. Place into oven and bake until edges are golden brown but center is still moist, about 7-8 minutes.
Remove from oven and cool on a wire rack.