Preheat oven to 350°F (175°C) and line two baking sheets with parchment. In a large bowl, stir melted butter, brown sugar, and granulated sugar until combined. Add egg and vanilla, stirring until smooth.

Sprinkle flour, baking soda, and salt over the wet mixture; stir just until no dry streaks remain. Fold in oats and toffee bits until evenly mixed.

Drop rounded tablespoons of dough (or use a medium scoop) onto the prepared sheets, spacing 2 inches apart, leaving them in tall mounds. Bake 12-14 minutes until edges are golden and centers look a little soft. Cool on the sheet 5 minutes, then transfer to a wire rack.