Maybe it is because I work a lot with pastries, that I was struck by the idea that the thickening of the egg sauce would be better controlled using a bain marie method (bagno maria in Italian), rather than the traditional: drop it all in the still hot pan and let the residual heat cook the sauce. Which of course means that the thickness of the sauce will depend on the type of pan you have and the amount of pasta you drop into the pan, as well as the heat loss of the pasta during the transfer. Normally, this means that the the sauce will be quite raw. And many traditionalists like it that way. On the other there are also many Italians that won't touch a soft boiled egg. They prefer applying more heat to the pan, which generally results in scrambled eggs and pasta. And some Italians actually prefer it this way! A lot more than you would think.
What I find is that best technique is to use a heat proof bowl to combine all the ingredients of the sauce. Roughly that is per person: 1 whole egg, a GOOD two pinches of parmigiano or pecorino cheese, 2-3 good twists on the pepper grinder, a good dash of olive oil, a pinch of salt (though I prefer to season almost entirely with heavily salted pasta water after) and the sauteed zucchini and onions, or pancetta if making the other version. Then when the pasta is done(more on this in a moment) transfer into bowl quickly, stir and check the consistency of the sauce. Add more pasta water if dry. And place the bowl on the still boiling pot of pasta water(best if the bowl is out of the water) and stir, cooking until the sauce has a good consistency. Good consistency? Well what I find satisfies most people is to cook the sauce until it begins to clump on the base of the bowl, remove the bowl stir vigorously to break the clumps on the bottom. And you should have a sauce that is creamy, smooth and on the verge of being completely cooked but not there yet. Since this is a dish I like to cook for friends, who always have conflicting opinions on how cooked the eggs should be, this is a good solution.
Important note!: this will only work if the pasta is cooked al dente if you over cook the spaghetti they will break with all the stirring and adjusting in the bowl. Really, if you want to serve them al dente you should remove them a good 30 - 60 seconds before they are al dente as they will finish in the bowl.