How long do you cook a custard after you add cornstarch?
I would argue that it is the gentler methods like Doug suggested which create problems. They are intended for eggs only custards, not eggs-and-starch. If you use them, you risk that your mixture doesn't get hot enough. Then your starch stays uncooked, and your eggs' starch-digesting enzymes stay intact and can liquefy everything. 

If you use either starch only, or a mixture of eggs and starch, your custard has to boil. I slurry the starch with a bit of the milk, never tried it with the eggs. Then add the slurry to the almost-simmering milk (which already contains sugar and flavors), and pour in the tempered eggs afterwards if using them. From the time the starch hits the liquid, you have to stir constantly or you risk burnt bottom, so you don't want to do it too early, but if you do it too late, the stream of slurry will start gelatinizing before it has been dispersed in the milk, and will clump. So, do it just before simmering, or if it has started to simmer, take it off the heat, mix it there, then back on the heat. 

After you have the slurry well mixed in, you simply stir slowly until after it has blubbed. You will notice a moment when it goes from liquid to thick, this is when the starch starts gelatinizing. Less than a minute later you should see the boil bubbles, which are very large and slow-forming in the viscous liquid. That's the time to take it off the heat, your starch is fully cooked and will not taste chalky. If you are serving it for a fussy occasion, it makes sense to pass it through a sieve to catch stray clumps of starch or egg protein, but I usually don't bother. 

If you were trying to keep the eggs from overcooking, that's impossible. Eggs overcook at around 87 C, while starch gelatinizes around 96 C. Also, the yolks will eat up your starch after 24 to 48 hours if not heated well. So you cannot keep the taste of a starchless custard if you use starch. That's not a problem texture-wise, since the starch takes care of the texture and you don't get the corning or whey exudate associated with overcooked egg custards.