I separate eggs with my hands, I'm pretty good at whites going one place and yolks going another. What's got me stumped is the chord. It seems to want to stay with the yolk, but it tends to hold on to quite a bit of the white. Should I let it stick to the yolk, pull it away, or what? Does it contain any fat? If I keep it with the whites, will it keep the whites from whipping as fully as possible?
The function of the chord, that is attached to the yolk, is to hold the yolk into place. To have the most uniform baking possible, you remove the chord. However, I never do. I keep it in with the rest of the whites and I've never had any problems with the finished products.
So you can:
- toss it
- keep it with the yolk (a little bit of whites with the yolk is not bad, the other way around is)
- keep it with the whites since it does not contain fat, it will not stop the whites from being whipped
It's up to you.
There is no reason to try to remove the chalazae by hand in practice, or to worry about whether it goes with the whites (it will not interfere with foaming) or the yolks.
The only application where they might be perceptible is a custard or curd. Simmered custards should be strained after cooking to catch any curdled bits; baked custards should be strained before baking to catch any undissolved bits (like sugar clumps or bits of zest). Either way, they will be caught in the straining.
They are essentially imperceptible in any other application. No one has ever sent a sunny side up egg or scrambled egg order back because of the chalazae.
There is a reason that, at least in the few hundred books I have personally read or episodes I have watched, no cookbook author or television cook has ever mentioned removing the chalazae by hand.
Sometimes you should remove the chalazae even if you're not separating the eggs. Case in point, I made lemon curd tonight to top a cheesecake. The curd contained two eggs and one yolk. The recipe said that it might be necessary to strain the curd before chilling. It was. After straining, it was clear that it was the chalazae (in minute pieces) still sitting in the sieve. So, after this learning experience, I would recommend plucking out the chalazae any time you are going for a smooth, translucent final result (think curd or pecan pie filling).
Another couple applications in which I've been able to occasionally detect the egg's chalazae in the finished product: ice cream and fresh mayonnaise. Straining the custard before freezing it takes care of the problem in ice cream. In mayonnaise, I almost never bother removing it because separating the chalazae while keeping the yolk intact is hard to do. Also, from what I've seen, the fresher the egg is, the stronger the chalazae is and the more you might want to think about removing it. But like others have said, it's pretty much impossible to notice most of the time unless your finished product is something that's meant to be super-smooth in texture.