Puree the strawberries in a blender or food processor - I recommend fresh strawberries if in season, otherwise frozen strawberries that have been defrosted will work. Approximately 1 cup of strawberries will yield a 1/2 cup of puree.
In a small mixing bowl, add the egg yolk, cornstarch, and the strawberry puree. Stir together until the cornstarch is dissolved.
In a small saucepan, add milk and sugar. Heat over medium heat until small bubbles start to form along the sides of the pan. Do not boil.
Temper the egg yolk - While whisking constantly, slowly drizzle about half of the heated milk into the strawberry/cornstarch mix. Then transfer the tempered strawberry mix back to the saucepan.
Continue to heat the pudding, over medium heat while whisking constantly, until the pudding starts to thicken and bubble. Remove the pudding from the heat and stir in the butter and vanilla extract.
Optional - Strain the pudding through a fine mesh strainer set over a bowl. This will remove any lumps or seeds from the pudding.
Transfer the pudding equally into your serving glasses. Cover with plastic wrap, with the wrap directly touching the pudding. This will keep a skin from forming. Refrigerate for 4 - 6 hours, or overnight, to allow the pudding to thicken even more.