Dissolve cornstarch in a small amount of milk.
Add the remaining milk and sugar to a small, thick-bottomed saucepan and bring to a boil over medium heat, stirring constantly.
Once boiling, add the cornstarch dissolved in milk in a thin stream, stirring constantly, and simmer, stirring constantly, until thickened, about 2 - 3 minutes.
Take the cornstarch syrup off the heat, add vanilla and stir. Let the cornstarch syrup cool to room temperature, stirring occasionally.
Beat softened butter until fluffy and white, about 3 - 4 minutes.
Add the cornstarch syrup in batches, whipping each time to a homogeneous mass so that you end up with an airy cream.
Add rum or cognac and whip again briefly.