Preparation

• Heat the milk in a heavy 3-quart saucepan over medium heat until very hot. If a skin forms on the milk’s surface, remove it. Meanwhile, beat the eggs, egg yolks, and salt in a medium bowl with an electric hand mixer on medium-high speed until slightly thickened, about 3 minutes. With the mixer on medium-high speed, add the sugar, 2 to 3 tablespoons at a time, beating about 30 seconds between additions. Continue beating until the mixture is very thick and pale, about another 3 minutes. On low speed, beat in the rum, vanilla, and cornstarch until smooth. Still on low speed, slowly add the hot milk, just a few dribbles at first and then in tablespoon-size dollops, beating after each addition only until smooth.
• Scrape the mixture into the saucepan used to heat the milk and add the cold butter pieces. Set the pan over medium heat and stir constantly and gently with a heatproof rubber spatula, scraping all across the bottom and around the sides of the pan. As the mixture heats, it will thicken first at the bottom of the pan, and the mixture will look very lumpy. Decrease the heat slightly and keep stirring as the entire mixture approaches the boiling point and becomes even thicker and lumpier. Switch to a whisk and stir (don’t beat) to smooth the pastry cream. The custard won’t actually boil because it’s so thick. When very thick and smooth (after 7 to 8 minutes), reduce the heat to very low and continue stirring gently with the rubber spatula all over the bottom and sides of the pan for another 1 minute.
• Remove the pan from the heat and immediately scrape the custard into a medium bowl. Lay a piece of plastic wrap directly on the custard’s surface, let cool to room temperature, and then refrigerate overnight.