Preheat oven to 350°F. Line 2 baking sheets with parchment paper. Arrange oven racks in the top and bottom thirds of your oven. If your eggs are not already at room temperature, place them in a bowl of hot water for 5 minutes (this will bring the temperature down).
Break the chocolate apart and place in a small saucepan. Add the butter and set over low heat. Melt the two together, stirring occasionally, until the chocolate is just melted. This should take about 5 to 7 minutes over low heat.
Meanwhile, beat the eggs and sugars in a stand mixer fitted with the whisk attachment for exactly 5 minutes.
Combine flour, cocoa powder, baking powder, and salt in a separate bowl and whisk to combine. Don't forget to stir the chocolate and butter melting on the stovetop.
Once the eggs and sugars have been whisking for 5 minutes exactly, warm the heavy cream in a small bowl in the microwave for 15 seconds. Stir in instant coffee.
Scrape down the bowl with sugars and eggs, and add the cream mixture and vanilla. Beat 15 seconds on high speed until combined.
Once the chocolate has finished melting completely, add it to the egg and sugar mixture. Beat 30 seconds or until fully combined. Scrape down the bowl.
Remove the bowl from the stand mixer and fold in the dry ingredients by hand using a wooden spoon or rubber spatula until no streaks of flour remain.
The dough will be rather loose, but it's supposed to look this way. Scoop the dough (I like to use a 2 Tbsp cookie scoop) onto prepared baking sheets, spacing them about 3 inches apart. Sprinkle each cookie with flaky sea salt before they bake.
Bake 12 minutes. Cool completely on pan, or eat warm straight off the pan :)