Melt butter and chocolate in a heavy bottomed saucepan over medium heat stirring constantly.
Once the chocolate is melted and smooth, stir in the sugar, eggs, salt, and vanilla extract. Whisk until smooth. Add the flour and stir until thoroughly combined. Fill muffin cups 1/2 full, using a teaspoon or a mini-scoop. Sprinkle each cup with a generous sprinkling of walnuts, if desired.
Bake for 15-20 minutes or until tester comes out mostly clean. Take care not to overbake. Remove from oven and let cool completely on wire rack. Once cool, use a butter knife to remove from pan and prepare frosting.
In the bowl of a stand mixer, whip butter until light and fluffy. Add remaining ingredients and pulse slowly to combine. Once combined, beat 5-7 minutes. Add additional whipping cream or confectioners sugar as need until desired frosting texture is met. You may also add additional cocoa for a stronger chocolate flavor.
Using a piping bag with a star tip, drop a dollop of frosting on each cooled brownie. Store in an airtight container for up to 3 days, refrigerating if needed in warmer temperatures.
Source: Brownies: Food Network Frosting: Lemon Sugar original