In a small bowl combine egg yolks, cornstarch, salt, and half of the sugar (2 Tablespoons). Whisk to combine.
In a medium saucepan, combine milk and remaining 2 tablespoons of the sugar. Heat over medium heat until mixture comes to a simmer.
Spoon a small amount of the hot milk mixture into the egg mixture and whisk to combine. You want to bring up the temperature of the egg mixture slowly to make sure the eggs do not scramble. Once the egg mixture is warm to the touch, add back into the milk mixture and whisk to combine.
Continue whisking vigorously and cooking over medium heat until mixture comes to a boil and begins to thicken. Cook for an additional 2-3 minutes to make sure cornstarch has been cooked out.
Remove pastry cream from the heat and whisk in the butter and white chocolate. Whisk to combine until all the butter and chocolate have melted and are combined well with the cream.
Place the cream in a bowl and cover with plastic wrap so that the wrap is directly on the pastry cream. This will make sure that a skin doesn't form on the top of the cream.
Place pastry cream in the refrigerator and cool completely before using to fill eclairs.
Once mixture has cooled completely, transfer it to a pastry bag with a small rounded tip or a zip top bag with a small corner cut off.
Cut a small hole in the end of the eclairs and pipe the pastry cream into the eclairs until it fills through the middle.