Leave the butter to soften at room temperature. Beat the eggs and add the sugar. Beat until whitened. Bring the milk to a boil and pour it in a thin trickle to the egg mixture while stirring nonstop.
Let the mixture heat up without boiling, still stirring nonstop, until you see small bubbles form on the surface. Remove from the stove and cool at room temperature.
Beat the softened butter to a cream and while stirring nonstop pour in the egg mixture 1 tbsp at a time, stir and add the next one.
Add the cognac and vanilla, stir and use it for cakes and layer cakes.