1. Preheat the oven to 410°F (210°C) and line two large baking sheets with parchment paper or silicone baking mats. Position the racks in the upper and lower thirds of the oven.

2. In a stand mixer fitted with the paddle attachment, beat the cold, cubed butter with the brown sugar and granulated sugar on medium-high speed until the mixture looks lighter in color and slightly creamy, with most of the butter worked in.

3. Add the cold eggs one at a time, mixing just until each is incorporated, then mix in the vanilla extract. Scrape down the sides and bottom of the bowl as needed.

4. In a separate bowl, whisk together the all-purpose flour, cake flour, cocoa powder, cornstarch, baking soda, and fine sea salt until evenly combined.

5. Add the dry ingredients to the butter mixture in two additions, mixing on low speed just until a thick dough forms and no dry streaks of flour remain.

6. Using a spatula, fold in most of the semisweet chocolate chunks and toffee bits, reserving a small handful of each for topping the cookies.

7. Portion the dough into large mounds about 3–4 tablespoons each, using a large cookie scoop or your hands. Keep the tops rough and craggy for that bakery-style look, and place the dough balls on the prepared baking sheets with plenty of space between them.

8. If time allows, chill the shaped dough in the refrigerator for 20–30 minutes to help the cookies bake up extra thick and gooey in the center.

9. Press a few of the reserved chocolate chunks and toffee bits onto the tops of each dough mound. Bake for 9–11 minutes, rotating the pans halfway through baking, until the edges are set and the tops are puffed but the centers still look slightly underbaked.

10. Remove the cookies from the oven and immediately sprinkle with flaky sea salt. Let them cool on the baking sheets for at least 10–15 minutes so the centers can finish setting before serving warm or transferring to a wire rack to cool completely.