This is the classic procedure:
Place 95% of the milk (or milk and heavy cream mixture) in a sauce pot with half the sugar, in another bowl, mix the remaining milk with the cornstarch and stir well, add the egg yolks and the remaining sugar; stir until homogeneous. Must be lump free (strain if needed).
Bring the liquid to a boil and temper the egg yolk - slurry. Return the heat and bring to first boil while stirring constantly. Take the pot off the heat and stir the butter in; cool off and cover with plastic to avoid a film.
The problem with this method is that it is very aggressive on the egg yolk and the cornstarch. Egg yolks begin to coagulate at 80 degrees Celsius / 175 degrees Fahrenheit and cornstarch coagulates between 80 and 85 degrees Celsius / 175 and 185 degrees Fahrenheit. The theory was that the mixture did not need to come to a boil after tempering the egg yolks in (which is what would over-coagulate the yolks and the starch, resulting in a lumpy, grainy cream), if you could get the liquid (milk or milk and heavy cream) hot enough to coagulate the yolks and the cornstarch in one quick shot.