Heat the milk in a medium stainless-steel saucepan over medium heat and bring almost to a boil. Remove from the heat.
Beat the egg yolks and sugar on medium-high speed in the bowl of an electric mixer fitted with the paddle attachment until pale and thick, about 5 minutes. With the mixer on low speed, sprinkle on the cornstarch. Beat on medium-low speed until combined, scraping down the bowl with a rubber spatula.
With the mixer on low speed, slowly pour the hot milk mixture into the egg mixture. Pour the mixture back into the pan. Cook over low heat, stirring constantly, until the mixture thickens, 5 to 7 minutes. (Pay attention because it will thicken and then quickly become scrambled eggs!)
Immediately, pour the mixture through a fine sieve into a large bowl. Stir in the vanilla, Cognac, butter, and heavy cream. Place plastic wrap directly on the custard and refrigerate until cold.