Line two baking sheets with Silpat baking mats or parchment paper and set aside.
Cut one stick (1/2 cup) of butter into tablespoons. Place in a medium skillet. Melt the butter over medium heat, swirling it in the pan occasionally. The butter will foam and pop, so be careful. Continue to swirl the pan often. Remove pan from heat once the butter starts to brown and smells nutty. There will be small brown bits on the bottom. The butter should be an amber color. Pour butter into a small bowl and cool to room temperature, about 20 minutes.
While the brown butter is cooling, in the bowl of a stand mixer, combine the remaining 1/2 cup butter with dark brown sugar and granulated sugar. Beat until creamy and smooth, about 3-4 minutes. Add the cooled brown butter and mix until smooth.
Add the egg, egg yolk, and vanilla and mix until combined.
In a medium bowl, whisk together flour, cornstarch, salt, and baking soda. Gradually mix in the flour on low speed until just combined. Stir in the chocolate chunks and toffee chunks.
Form the cookie dough into a large ball and wrap in plastic wrap. Chill for at least 30 minutes.
When ready to bake, preheat oven to 350 degrees F. Remove dough from fridge and form into 2 tablespoon sized cookie dough balls. Place on prepared baking sheets, about 2 inches apart. Sprinkle with sea salt.
Bake cookies for 10 minutes or until slightly brown around the edges. Remove from oven and allow the cookies to cool on the baking sheet for 2-3 minutes. Transfer to a wire cooling rack and cool completely...or eat a warm cookie! I won't tell:) Store cookies in an air-tight container for 2-3 days. These cookies also freeze well.