Melt baking chocolate: I like to do so in a glass bowl in the microwave, but doing so on the stove top over low heat is another option.
Either way, melt until smooth, remove from heat, and allow to cool to almost room temperature - but not solidifying.
In the meantime, beat together butter and sugar in a stand mixer - or with an electric mixer - until pale and fluffy. Add cocoa powder and vanilla, beat on low until blended.
Add cooled chocolate, beat once more until completely blended in.
Take one egg from the fridge or freezer, crack it into the mix, and beat until mixed in. Turn speed up to medium-high, and beat for 4-5 minutes.
Repeat with remaining eggs - 4-5 minutes apart. Leave eggs chilling while waiting to add them. Once final egg has been beaten for 4-5 minutes, cover bowl with plastic wrap, chill for at least one hour.
Spoon a small amount of frosting into a pastry bag fitted with a star attachment, pipe stars onto cooled cake.
Refill bag with small amounts of frosting as you go - having too much in the bag at one time will have the frosting being warmed from your hands.
If frosting is/becomes too runny to pipe, return to fridge to cool / firm up for a bit.
Once top of cake is covered in piped stars, scatter chocolate sprinkles on top (if desired), cover, and freeze.
Slice and serve straight out of the freezer, or allow slices to thaw slightly before serving.