Brown the butter before doing anything else, as it needs time to cool: Add the sliced butter to a stainless steel or light-colored skillet or saucepan. Turn to medium heat. Swirl the pan or stir with a silicone spatula occasionally until melted, foamy, and at a bubble (it should take 2 ½ to 3 minutes).Heat for 2 to 3 more minutes, stirring frequently with a silicone spatula until nutty in aroma and slightly darker. Turn off the heat before it starts foaming up the sides of the pan.Immediately pour into a medium heatproof bowl to stop cooking, scraping out all of the butter from the pan with the spatula.Refrigerate for 20 to 25 minutes or until no longer warm. And add a large plate or sheet pan to the fridge to chill. In a small bowl, combine the flaxseed meal with 5 tablespoons (70 mL) of warm water. Whisk well to combine and rest for 15 minutes, whisking again halfway through and once more at the end of the 15 minutes.
While waiting for the butter and flax egg, coarsely chop the chocolate and set aside. If desired, reserve 12 pieces of chopped chocolate to press into each cookie.
In a medium bowl, combine the dry ingredients: flour, salt, baking soda, and espresso powder if using. Whisk well to incorporate.
Once flax eggs have gelled and brown butter has cooled, add both to a large bowl. Add the brown sugar, cane sugar, and vanilla. Use an electric mixer on medium to mix everything together until well combined and small waves appear, about 30 seconds (or use a whisk and arm power for ~45 seconds).
Remove the beaters and switch to a silicone spatula. Add half of the dry ingredients into the wet. Fold with a silicone spatula until just combined. Add the rest of the dry ingredients and chopped chocolate (minus reserved 12 pieces, if desired). Fold just until no dry spots remain. The dough should be thick but somewhat soft, not stodgy.
Scoop out cookie dough rounds. Use a large cookie scoop to measure out ~72g per cookie dough round (or use a ¼ cup measuring cup, leveling off the top & using a small silicone spatula to get the dough out of the measuring cup). PS: Don't make smaller cookies (see Note 5). Remove the plate/pan from the fridge and line with parchment paper. Scoop the cookie dough balls onto the plate/pan. No need to space them out, as they’re going to chill first. If desired, press a piece of chopped chocolate into the top of each cookie.NOTE: If the dough is too sticky, chill for 10-30 minutes, then shape. Refrigerate the pan. Once the cookie dough balls have set, you can transfer them to a ziploc bag and refrigerate. Refrigerate for 24 hours (or up to 72 hours), or 8 hours at a minimum (see Note 6).
When ready to bake, preheat the oven to 350ºF / 175ºC and arrange a rack in the center of the oven. If your rimmed sheet pan is not well-worn or not made of aluminum or nonstick, line it with parchment paper to prevent sticking (see Note 7). Add six cookie dough rounds, spacing them 3 inches (7.5 cm) apart, as they’ll spread a lot.
Bake for 14 to 16 minutes, until edges are golden brown and a bit set but still gooey and soft in the center (16 minutes for a slightly crispier edge).
While still warm, sprinkle a little flaky sea salt. Cool in the pans for 10 minutes (5 minutes if lined with parchment), then transfer to a cooling rack to cool for a few more minutes.
Bake the remaining batch (or freeze the cookie dough to bake later).