Blend the strawberries until smooth. You want a vibrant pink puree with no big chunks hanging around.
Strain the puree if you want ultra-smooth pudding. This step is optional but worth it if you hate seeds.
Whisk sugar, cornstarch, and salt in a saucepan. This helps prevent clumps later.
Slowly add milk and strawberry puree, whisking constantly so things stay silky.
Cook over medium heat, stirring nonstop. The mixture will thicken suddenly—don’t walk away.
Remove from heat and add vanilla. Stir it in like you mean it.
Pour into serving dishes, cover, and chill until set.