Preheat the oven to 375°. Grease an 8-inch round baking pan all over the bottom and sides. Line the bottom of the baking pan with a round piece of parchment paper.
Melt chocolate in a sauce pot: melt butter first over low heat and then add chocolate chips. Keep slowly stirring the whole time and when chocolate chips are about half way melted. Take the sauce pot off the heat and continue to stir until the chips are fully melted and the mixture is smooth. ORMelt chocolate in a microwave: place butter and chocolate chips in a microwave-safe bowl and heat on half the power, at 30 second increments. Make sure to stir after every 30 seconds.
Pour melted chocolate mixture into the bowl of the electric mixer and add sugar and vanilla extract. Beat for a few second until combined.
Beat in eggs, one at a time.
Once the eggs are incorporated, lower the speed and add cocoa powder, baking powder, salt, and espresso powder if using. Beat until all ingredients are evenly incorporated.
Spread the cake batter into the papered baking pan and sprinkle some coarse sea salt over the top.
Bake the cake for 30 minutes, take it out of the oven, and let it cool to room temperature before cutting. (P.S. If you like to have the center a little gooey, bake it for 25 minutes.)