In a medium saucepan melt butter over medium heat, then bring to a boil. Once butter starts boiling, swirl the butter around until the foamy phase pasees and becomes a deep amber color. Remove from heat and cool for 20 minutes.
While butter is cooling, preheat the oven to 350°F. Line a baking sheet with parchment paper, set aside.
In a large bowl whisk together flour, baking soda, and fleur de sel, set aside.
Add in brown sugar, eggs, and vanilla to the cooled butter in the saucepan and stir well to combine. Pour into flour mixture and stir using a spatula until dough has formed. Fold in butterscotch chips.
Using a cookie scoop, set the dough 2 inches apart on the baking sheet. Bake for 10-12 minutes until the edges are lightly golden. Immediately after taking out form the oven sprinkle fleur de sel lightly on each cookie.
Allow cookies to cool for 2-3 minutes on the baking sheet and then transfer to a wire rack to cool completely.
Sprinkle fleur de sel lightly on each cookie if more salt is desired.