Place the butter in a large saucepan and heat over medium until fully melted.
Increase the heat to medium-high and continue cooking the butter, swirling it gently in the pan and scraping the sides to prevent burning.
Once the bubbling slows and the butter turns a light golden brown with a nutty aroma, remove it from the heat and transfer to a large heatproof bowl. Allow to cool for 25–30 minutes.
While the butter cools, chop the Heath Toffee Bars and preheat your oven to 350°F.
When the butter has cooled, transfer it to a large mixing bowl. Add the brown sugar and granulated sugar, and mix with a stand or hand mixer until well combined.
Add the eggs one at a time, mixing on low speed after each addition. Add the vanilla extract and continue mixing on low speed.
In a separate bowl, whisk together the flour, cornstarch, and baking soda.
Gradually add the dry ingredients to the butter mixture, mixing on low speed until just incorporated.
Fold in the chocolate chips and chopped Heath Toffee Bar pieces using a silicone spatula until evenly combined.
Line a baking sheet with parchment paper. Scoop 1 to 1 ½ tablespoon portions of dough onto the baking sheet, spacing them 2–3 inches apart.
Bake for 10 minutes, or until the edges are golden brown and the centers remain soft.
Remove from the oven and immediately sprinkle with sea salt.
Allow the cookies to rest on the pan for 1–2 minutes before transferring them to a cooling rack to cool completely.