See Pastry Cream Recipe for the full step-by-step recipe.
The milk and sugar mixture takes a long time to boil over, so instead of getting everything ready first and then putting the milk and sugar on the stove, to save time get everything ready while you wait. I promise you will get it done in plenty of time and will still have to watch the milk mixture. Make sure to also check on it frequently because it can boil all the over and out of the pan. Once it starts to rise slightly and bubbles start forming on the sides of the pan. that is exactly when you pour in the egg and cornstarch mixture.
Why pour it into a sheet pan? – It just helps the cooling process and shocks the mixture evenly, helping to make the right consistency.