Preheat the oven to 350°F (175°C). Grease a 9" x 13" x 2" baking pan. If you like, line the pan with parchment paper and grease the paper.
Whisk together the flour, baking soda, and salt. Set aside.
Using an electric mixer on medium speed, beat the butter, sugar, and brown sugar until light and fluffy. Add the eggs, one at a time, mixing well after each addition.
Add the melted chocoalte and vanilla, and mix until combined.
Reduce the mixer speed to low. Add the flour mixture in three portions, alternating with two portions of the buttermilk. Mix in the sour cream. Don't over-mix; only mix just until combined.
Transfer the batter to the prepared pan, and spread evenly. Tap the pan gently on the countertop a few times to dislodge air bubbles.
Bake 35 to 40 minutes, or until a pick inserted into the center of the cake comes out clean.
Place the pan on a wire rack, and allow the cake to cool completely before frosting.
To make the frosting:
Using an electric mixer on medium speed, beat the butter until light and fluffy.
Reduce the mixer speed to low. Gradually add the confectioners' sugar, cocoa powder, cream, vanilla, and salt. Mix until thoroughly combined and fluffy. If needed, add a small amount of cream to thin the frosting or confectioners' sugar to thicken the frosting.
Spread the frosting over the top of the cooled cake. Decorate with sprinkles.
Notes
Store the cake in an airtight container at room temperature up to 3 days or in the freezer up to 3 months.