Brown butter in a small saucepan, stirring constantly over low-medium until it gets foamy and it starts to turn an amber/honey color. Remove from heat and pour into a separate bowl and place in the refrigerator until solid but softened.

Beat butter, both sugars, and vanilla extract until light and fluffy. Add in flour and salt, mix until just combined. There will be large pieces of dough. Fold in toffee pieces

Divide the dough in half and roll each half into a 6 1/2-inch log, using the plastic wrap to help shape the soft dough. Wrap logs tightly in plastic wrap and chill for 1 hour in the refrigerator.

Preheat oven to 350°F and grease cookie sheet and line with parchment paper so it sticks. Using a sharp knife, cut logs into ¼ - inch rounds. Place rounds 2 inches apart on cookie sheets. This part is optional, but you can gently press rounds with the bottom of a flat bottom glass to make them level. Chill for 20 minutes in the refrigerator.

Bake for about 15 minutes, rotating pans halfway through, until very lightly golden and edges are set. Cool for 5 minutes on cookie sheets, then transfer to a wire rack to cool completely.