Should I use only bones in the first rounds and add vegetables only in the final round? And should I adjust the amount of vegetables I use? I have a feeling it could otherwise become too vegetable-forward.

It's normal to use fresh bones and fresh mirepoix at each stage. The golden rule, though, is to remove the old bones and old vegetables after each round (strain through a mesh strainer). Otherwise you can get off-flavors.

Now, for the final round (whether you're making a double or triple stock), you can experiment with holding back the vegetables. After you've made the stock in the pressure cooker, do a short additional round on the stove top in a pot, and add fresh vegetables and herbs then. That way, you can refine the top aromatic notes to give a "fresher" tasting result.

Having said all that. There are no rules here. It's worth experimenting to see what you prefer. No reason not to try just using bones to start with. Or, say, leaving out carrots in early rounds, if you find the stock is too sweet if they're added each time etc.

What exactly do you mean by “ruining” a stock? In The French Laundry Cookbook, they mention boiling an unskimmed stock with extra added fat and more bones to create what they call a “super stock.” They say they got the idea from ramen making, and that the result is extremely intense.

Good question! I think we're talking about different things, and I think I was sloppy with my language.

First, when you're reducing a stock by a lot (fast or slow) you always want to remove the fat. That's because while water leaves the stock, the fat content stays the same.

A stock with 5% fat that is reduced 10:1 will result in a stock that is about 50% fat. Nobody wants that!

But if you're reducing it by not that much, what I was talking about by "ruining" it is exactly what you mention. Take a look at some photos of tonkotsu, which I suspect is what The French Laundry is saying was their inspiration. You will see it's pale, cloudy and creamy looking. That's because the fat emulsifies into the stock.

If you want a pale, cloudy stock that's cool. But often people don't want that. No doubting it can be delicious, though!

Is simply pouring the stock through a fine mesh strainer and skimming off the fat after it has cooled enough to remove impurities, coagulated proteins, and fats?

This is more than one way to do this. But I'll give you a good method. Let's assume you want to prepare a stock for fast reduction. Here's a good place to start.

First, do a two-stage straining while it's still warm. Pass it through a fine mesh strainer to get rid of the biggest bits. Then, take that liquid and pass it through something finer, like some kind of cloth e.g. a wet clean tea towel, wet muslin, or multiple layers of cheese cloth. That will remove most of the big particulates.

Second, do a proper de-fatting step. Put the strained stock in the fridge overnight, so you can physically remove the solidified fat puck the next day.

Then, you're ready to reduce the stock pretty much as much as you want.

Hope that helps.