I was at the Big Sur Bakery (the restaurant referenced in the recipe link from the NY Times) several weeks ago. I was allowed to see their oven and their method for the breakfast pizza with an egg.
They par bake the pie first with the cheese on it and then pull it out, add the egg and the bacon and put it back in the oven for a few minutes.
The par baked pie with the cheese is obviously hot along with the crust thus allowing the egg to cook and not to spill or have the yolk roll prior to placing in the oven for the finish baking. Their oven is a very, very large old brick oven, not ideal for pizza by way of its design, but they use it for many other baked goods and other things as well. Their oven temp seems to be quite low thus the par bake and adequate time for cooking the egg without burning the crust.
It is a very good pizza, especially for breakfast. I had one in the past with sausage, egg, and jalapeno and it was wonderful. I think when it warms up I will try it at home.