Butter then line with parchment paper the bottom of an 8" springform pan or the bottom of a round 8" cake pan. Preheat oven to 350 F.
Chop the chocolate and place it in a large, heat proof mixing bowl. Set aside.
Next, brown the butter. Melt the butter in a medium skillet over medium heat. Stir occasionally at first. Once begins to bubble and comes to a boil, stir it constantly. It will start to foam. Continue stirring as you watch for it to turn a light, amber color and develop a nutty smell which should happen in about five minutes. Pour the brown butter over the chopped chocolate. Make sure the scrape the bottom of the pan for all the bits.
Stir the chocolate and brown butter together until the chocolate has melted. Sift the cocoa into the butter and chocolate mixture. Whisk in the sugar and salt. Whisk in the eggs one at a time. Add the vanilla extract. Make sure mixture is well mixed.
Pour mixture into prepared pan. Spread evenly and bake for 25-27 minutes or until an instant read thermometer reaches 200 degrees Fahrenheit. Serve warm or at room temperature. Top with chocolate whipped cream. Alternatively, you can top the cake with a dusting of powdered sugar or cocoa powder or serve it with ice cream.
Chocolate Whipped Cream (optional)
Combine all the ingredients in the bowl of an electric mixer or in a large mixing bowl. Use a stand mixer or hand held mixer fitted with the whisk attachment to mix the ingredients on medium speed til thickened, about 1-2 minutes, then increase speed to medium-high and mix 30-60 more seconds until soft to medium-stiff peaks form. Do not overwhip. Enjoy immediately or refrigerate til ready to use.
Notes
Butter: I recommend browning the butter. Brown butter adds an extra layer of toasty, nutty flavor. To skip this step, simply melt the butter and chopped chocolate in a microwave safe bowl in 20 second bursts. Stir well in between each interval. Continue until chocolate has melted. You could also place the chopped chocolate and butter in a bowl over a pot of simmering water to melt it. Make sure the bottom of the bowl doesn't touch the water and be sure to stir occasionally as the mixture melts. Chocolate: Dark or bittersweet chocolate can be used in place of semisweet. Use good quality chocolate. I would not recommend chocolate chips. Espresso powder: Add an optional 1 to 1 and 1/2 teaspoons of espresso powder to the dry ingredients to enhance the chocolate flavor. Topping options: Whipped cream is optional. Swap in regular whipped cream in place of chocolate whipped cream. You can also dust it with powdered sugar or powdered sugar before serving or top with ice cream! Storage: Store this cake in an airtight container in the fridge for up to 4 days. You can freeze this cake in a freezer safe container for up to 2 months.