I was taught by food safety classes (over 10 years ago though) to put it in a container that allows it to be no deeper than 4 inches and place it in the fridge or freezer.
If you leave it in the pot (or a deep container) to cool the middle will stay warm for a very long time and allow bacteria to grow

You're right; my apologies to the recipe writer. It does say to transfer to a shallow metal pan to cool in the refrigerator. It seems like that would still release a ton of heat into the fridge. And is this really necessary? I've always let large pots of soup, stew, etc. cool on the stove before putting them in the fridge; then I make sure to heat to a simmer for a few minutes before eating.

What a weird cooling method... sticking it immediately in the refrigerator can cause bitter tastes.

Chefs use shallow jelly roll pans to cool things quickly, then transfer the food into a different container for refrigeration. A lot of dishes, but a foolproof method.

They probably suggest the quick cool for food safety reasons.

Recipe says to bake at 325 for 2.5 hours, let sit for 10 minutes, and then serve or cool quickly (by setting pan in cold water or the fridge). Why would I need to do this? It's a pork braise; it seems unlikely that it would overcook from residual heat. Not to mention I don't think there really is a way to cook it quickly, short of sticking it in an industrial freezer.