Preheat the oven to 350°F (175°C) and line two baking sheets with parchment paper.
Beat softened butter with brown and granulated sugar until light and fluffy, about 2–3 minutes. Mix in the eggs one at a time, then stir in vanilla.
In a separate bowl, whisk together flour, baking soda, and salt; gradually add to the wet mixture just until combined.
Fold in oats and toffee bits. For thicker cookies, chill dough for 30 minutes.
Scoop tablespoon-sized portions onto baking sheets, flatten slightly, and sprinkle with flaky sea salt.
Bake for 10–12 minutes until edges are golden and centers are set but soft.
Cool on the sheets for 5 minutes before transferring to a wire rack to cool completely.