Make the pudding: In a medium saucepan, heat 3/4 cup milk and sugar over medium heat until hot. In a small bowl, whisk remaining 1/4 cup milk, egg yolk, and cornstarch until smooth. Whisking constantly, add 1 tablespoon hot milk mixture to egg yolk until smooth. Repeat a total of 4 times, then add all back to saucepan. Stirring occasionally, bring pudding to a simmer and cook until smooth and thickened. Remove from heat and stir in vanilla and salt. Cool pudding at room temperature, then press plastic wrap directly on surface and refrigerate until cold.