Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
Brown the butter: In a saucepan over medium-low heat, melt the butter. Continue to cook, stirring occasionally, until the butter turns golden brown and smells nutty. Remove from heat and allow to cool in a glass bowl.
Mix sugars and butter: In a large mixing bowl, combine the granulated sugar, brown sugar and slightly cooled brown butter. Mix until well combined.
Add eggs and vanilla: Add the egg, egg yolks, and vanilla extract to the sugar-butter mixture. Mix until smooth and creamy.
Incorporate dry ingredients: In a separate bowl, whisk together the flour, cornstarch and baking soda. Gradually add the dry mixture to the wet mixture, stirring until just combined.
Fold in chocolate and toffee: Gently fold in the chocolate and toffee pieces until evenly distributed throughout the dough.
Chill the dough: Cover the dough and chill in the refrigerator for at least 30 minutes, or up to 24 hours. This helps prevent the cookies from spreading too much.
Form cookie dough balls: Using a cookie scoop or spoon, scoop out dough and place on the prepared baking sheet, leaving space between each cookie.
Bake the cookies: Bake for 10–12 minutes, or until the edges are golden brown. The centers may still look slightly undercooked, but they’ll continue to set as they cool.
Cool and enjoy: Top with flaky sea salt. Allow the cookies to cool on the baking sheet for a few minutes before transferring to a wire rack. Serve warm or at room temperature.