Preheat the oven to 375 degrees F (190 degrees C). Grease a 9x13-inch baking pan.
Make the brownies: Combine baking chocolate and butter in a microwave-safe bowl. Microwave on high until chocolate is soft and butter is melted, about 2 minutes. Stir to mix.
Beat eggs, sugar, and vanilla in a large bowl with an electric mixer on high speed for 2 minutes. Reduce the speed to low and beat in melted butter-chocolate mixture. Beat in flour until just combined; do not overmix. Stir in chopped walnuts. Spread batter in the prepared pan.
Bake in the preheated oven until a toothpick inserted into the center comes out with fudgy crumbs, about 35 minutes. Let cool in the pan.
Meanwhile, make the frosting: Combine sugar and heavy cream in a saucepan over medium heat. Stir until sugar dissolves and mixture begins to simmer, about 3 minutes. Reduce the heat to low and simmer for 7 minutes without stirring. Remove from the heat.
Add baking chocolate and butter; stir until melted and chocolate is blended in. Whisk in vanilla until smooth. Place into the refrigerator and stir every few minutes until frosting is chilled and thick, about 30 minutes.