Add heavy cream and 1/2 cup milk to a medium saucepan. Place over medium-low heat. Heat the cream while working on the next step.
In a large mixing bowl, whisk together cornstarch, granulated sugar, egg yolks, and 1/2 cup milk until smooth.
Once the heavy cream/milk mixture starts bubbling at the edges of the pan (scalded), remove from the heat.
Very slowly drizzle the hot cream into the egg mixture, whisking constantly. Be sure to drizzle slowly and whisk quickly to temper the egg mixture so it does not turn into scrambled eggs.
Once all the hot cream has been added to the egg mixture, pour the custard mixture back into the saucepan and place on the stove over medium-low heat.
Whisk constantly until the mixture thickens and is bubbling about 3-5 minutes.
Remove the saucepan from the heat. Add in cold, cubed salted butter and vanilla bean paste. Whisk until the butter is melted and the pastry cream is smooth.
Pour the pastry cream into a fine mesh sieve over a large bowl. Use the back of a spoon to push through the pastry cream to remove any lumps. Work in small batches for best results.
Place a piece of plastic wrap directly on top of the pastry cream to prevent a skin from forming.
Chill for at least 4 hours before using. Store in the refrigerator for up to 3 days.