Place strawberries, milk, sugar, and cornstarch in a blender and blend until completely smooth, about 30–60 seconds.
Pour the mixture into a medium saucepan, scraping the blender sides to get it all out.
Stir in the vanilla extract and lemon zest.
Heat the saucepan over medium heat, whisking constantly to avoid lumps and sticking. After 4–6 minutes, the pudding will start to thicken. Keep whisking until it reaches a smooth, creamy consistency.
Pour into serving cups or bowls, let cool at room temperature for 10–15 minutes, then refrigerate for at least 2 hours until fully set.
Serve chilled, topped with whipped cream if you like.