In a medium saucepan, combine milk and 1/4 cup sugar over medium heat, and bring to a simmer. Meanwhile, in a medium bowl, whisk egg yolks and remaining sugar until well combined. Whisk in vanilla and salt. Whisk in cornstarch, 1 tablespoon at a time, until fully incorporated. While whisking egg mixture constantly, slowly add 1 cup of the heated milk to the egg mixture. Strain this mixture into milk remaining in saucepan. Continue cooking over medium heat, whisking constantly, until mixture comes to a full boil, 4 to 6 minutes.
Transfer to a medium bowl, and cover with plastic wrap, pressing wrap against the filling to prevent a skin from forming. Refrigerate until at least 3 hours and up to overnight.