Place the eggs and sugar in a mixer bowl and whisk by hand for 2 minutes to blend well.
Warm the milk to body temperature and stir half of it into the egg mixture.
Place the mixer bowl on the machine with the whip attachment. With the mixer running at medium speed, gradually incorporate the flour. Mix in the heavy cream, scrape down the sides of the bowl as needed, and continue mixing until you have a smooth paste.
On low speed, gradually add the remaining milk along with the salt, vanilla, and butter. The batter will be quite thin. Let the batter rest at room temperature for 1 hour.