In a stand mixer, cream together the softened butter, dark brown sugar, and granulated sugar on medium-high speed for 3–4 minutes until light and fluffy. Add the large egg and vanilla extract, mixing for an additional 30 seconds until well combined. Slowly incorporate the salt, baking powder, baking soda, and flour, mixing until just combined, then gently fold in the old-fashioned oats and toffee bits.

Using a 3-tablespoon scoop, portion the dough and shape into balls, placing a soft caramel in the center of each ball without pressing it in too deep. Line a baking sheet with parchment paper and lay the cookie dough balls on it. Cover and chill in the refrigerator for 2 to 24 hours.

Preheat your oven to 365°F (185°C) while the dough chills. Line multiple baking sheets with parchment paper, then arrange 6–8 chilled dough balls on each sheet, leaving enough space for spreading. Sprinkle a pinch of flaked salt on top.

Bake the cookies in the preheated oven for 10–12 minutes or until the edges turn golden brown. Remove and cool on baking sheets before transferring to wire racks.

Sprinkle extra flaked salt on top of the cookies right after they come out of the oven, if desired. Let cool before serving.