Preheat oven to 375°F and line a baking sheet with parchment paper and set aside. It is best if you use two baking sheets and rotate them for the batches. Dropping the second batch of dough on the hot cookie sheet will slightly change the structure of the cookie.
Pull the 14 tablespoons unsalted butter out of the refrigerator to sit at room temperature 15 minutes before using.
In a medium bowl, whisk together the 1¾ cup all-purpose flour, 2 tablespoons malted milk powder, 1 teaspoon salt, and ½ teaspoon baking soda and set aside.
Add 10 tablespoons of butter to a skillet and cook over medium heat until melted. Continue cooking and stirring frequently for 2 to 3 minutes until brown bits start to form in the bottom of the pan, the top is foamy, and it has a nutty aroma. Remove from heat and stir in the remaining 4 tablespoons of butter until melted. Transfer the butter to a large heat-safe bowl or stand mixer bowl fitted with a whisk attachment.
Add the ¾ cup dark brown sugar, ½ cup granulated sugar, and 2 teaspoons vanilla extract to the butter and mix to combine.
Add 1 large egg and 1 large egg yolk and mix for 30 seconds. Let rest for 3 minutes, then whisk again for 30 seconds. Repeat the resting and whisking for 2 more rounds. The batter should be smooth, thick, and shiny when done - almost like caramel sauce.
Use a rubber spatula or paddle attachment to mix the dry ingredients into the wet ingredients for 1 minute. The dough will seem very soft, this is normal and you do not need to chill it.
Fold in most of the chopped 1 cup dark chocolate chips and 1 cup Heath Bits 'o Brickle Toffee Bits, reserving a little to sprinkle on top of the cookies prior to baking.
Portion the dough out with a large (¼ cup sized) cookie scoop and drop the dough 3 inches apart on the prepared baking sheet. Top the scoops of dough with the remaining chopped chocolate and gently press it into the top. Sprinkle with flaky sea salt.
Bake for 8 to 10 minutes, rotating halfway through. The cookies should look slightly cracked and only slightly brown around the edge. Remove from the oven and allow the cookies to cool for 3 minutes on the baking sheet before transferring them to a wire rack to cool completely.