While the cheesecake is baking, make the pastry cream. Heat the milk, cream, and butter together in a large saucepan over medium-high heat just until it bubbles around the edge, stirring until the butter has melted and is incorporated. Remove from the heat. Meanwhile, beat the egg yolks, sugar, and cornstarch together in a large bowl with a mixer on high until the mixture thickens and turns light yellow, about 3 minutes. Reduce the speed to low and beat in about 1 cup of the hot cream mixture. Return this to the saucepan, stirring constantly over medium heat until the mixture thickens and comes to a full boil (watch carefully as this will take only about a couple of minutes). Remove from the heat and stir in the vanilla and food coloring. Immediately transfer to a medium-size bowl (this stops the cooking), place a piece of plastic wrap directly on the surface of the pastry cream (this prevents a skin from forming), and refrigerate until cold and set, at least 2 hours.