Cut the toffee bar into ¼" pieces and place in a bowl.
Preheat oven to 375°F.
Cook butter in a medium saucepan over medium heat, stirring often until it foams.
Brown 5-8 minutes, then scrape into a large bowl and let it cool completely. (Don't let it burn.)
In a separate bowl mix flour, baking soda, and kosher salt.
Add both sugars (brown and white) and mix well, then add to the brown butter to your mixing bowl. Use an electric mixer on medium speed to incorporate everything.
Next add the eggs and the vanilla, and beat for about 30 seconds. The mixture will begin to turn light and thicken.
Reduce the speed of the mixer to low, and begin to add the flour mixture gradually. Continue to beat until well combined. Remove the mixer blade.
Slowly add the chocolate wafers and the toffee pieces while mixing with a large spatula by hand. The dough will seem a bit runny.
Allow the dough mixture to rest at room temperature for about 30 minutes. This will allow the dough to thicken.
Line a cookie sheet with parchment paper.
Using a 1 ½ oz. ice cream scoop portion out 10 balls of dough onto the lined cookie sheet. The cookie balls should be about 3" apart since they will spread out.
Sprinkle with the flaky salt or coarse sea salt.
Bake in center rack for 9-12 minutes, or until the edges begin to turn golden. The center should be soft.
Remove from the oven and let them cool for about 10-15 minutes before transferring them to a cooling rack.
Place the remaining 10 balls on another parchment lined baking sheet, and repeat the baking procedure.