In a medium saucepan, heat the milk over medium heat until it starts to simmer, but don’t let it boil. Once it reaches a simmer, remove from heat and set aside.
In a separate large bowl, whisk together the egg yolks, sugar, cornstarch, vanilla extract, and salt until the mixture is smooth and lump-free. Gradually pour a small amount of the warm milk into the egg mixture, whisking constantly to avoid curdling the eggs. Continue whisking as you slowly add the rest of the milk.
Once fully combined, pour the mixture back into the saucepan. Place the pan over medium heat, stirring constantly, until the mixture thickens into a smooth custard, about 3–5 minutes. Be careful not to let it boil.
Once thickened, remove from the heat and set aside to cool while you prepare the churros.