In a light colored saucepan, melt the butter and milk powder over medium heat, whisking to combine. The mixture will look curdled (this is normal).
Continue cooking & whisking the butter mixture for about 5 minutes or until the milk solids begin to sink to the bottom and turn golden brown and the butter looks frothy.
Remove the butter from the heat immediately and pour it into a large glass mixing bowl. Set aside to cool.
While the butter is cooling, make the toffee. Prepare a small heat resistant plate or tray with parchment paper. Set aside. In a heavy bottom saucepan, melt the butter over medium heat. Whisk in the brown sugar and salt. Continue whisking vigorously and cooking the mixture for about 8-10 minutes. Do NOT stop whisking. The butter and sugar will be separated at first but will come together after a couple of minutes. Then, the color of the mixture will become more pale and look gritty. Finally, it will turn a darker color and become smooth, like peanut butter. (See the photos above.)
Remove from the heat immediately and pour onto the prepared plate. Set aside to cool.
In a medium mixing bowl, whisk together the flour, cornstarch, salt, and baking soda. Set aside.
Check the butter. If it has cooled to room temperature (about 70 degrees), proceed. If it is still warm, pop it in the fridge or freezer until it has reached room temperature. Once it has cooled, whisk the brown and granulated sugar into the butter until well combined.
Add the eggs, vanilla, and espresso. Whisk until smooth.
Pour all of the dry ingredients into the wet. Fold until the flour is about halfway combined.
Once the toffee is cool enough to handle, transfer it to a quart size zip top bag, breaking it in half if needed to fit. Seal the bag and use a rolling pin or heavy object to smash the toffee into small bits.
Add all of the toffee bits and the chocolate to the cookie dough. Continue folding just until all of the flour is absorbed.
Using a cookie scoop, scoop all of the cookie dough into either 1.5, 3, or 4 Tablespoon balls. (I used a 4 Tablespoon scoop.) Place on a baking sheet or plate lined with parchment paper that can fit in your refrigerator. Cover and wrap tightly. Refrigerate for 2 hours.
At the end of the 2 hour chill time, preheat the oven to 350 degrees. Arrange the dough balls on a baking sheet lined with parchment paper. (I fit 6 balls at a time on my sheet.)
Bake as follows depending on the size of your cookies. For 1.5 Tbs, bake for 10-12 minutes. For 3 Tbs, bake for 11-13 minutes. For 4 Tbs, bake for 13-15 minutes. The cookies are done when the edges are brown and the middle is puffy and soft. Do not overbake. If some of the toffee spills out of the cookies, use a butter knife or round cookie cutter to gently push it back and reshape the cookies. Sprinkle each cookie with the sea salt flakes. Cool for 5-10 minutes on the baking sheet or until set. Transfer to a wire rack to continue cooling.