To add to the discussion, I've had quite a few craft beers these last few years that were infused with coffee in one way or another. Cold-brewed, espresso, grounds at whirlpool, "dry beaning," etc... While some of these beers have been outstanding, the most common flaw I've found is many have that boiled or burnt coffee flavor/aroma. Remember grandma's old percolator and the shitty ass coffee that thing use to pump out?
On many occasions I've had the chance to talk to the craft brewers themselves about how they infused the coffee. With the beers that had that burnt/boiled coffee aspect, it seemed the majority had added grounds at whirlpool, when the wort was near boiling.
I did an experiment a few months back with 6 different brewing methods using the same coffee (Peet's Arabian Mocha Java). They were as follows:
1) Percolator - burnt flavor and aroma. One of the worst ways to brew coffee, IMO.
2) French press - very strong flavors and aromas. Slightly oily. More ashen flavors than the other methods.
3) Drip cone (Swissgold brand metal filter) - bold flavors an strong aroma. Faintly oily. No real ashen flavors.
4) Espresso - Extremely bold flavor and aroma. Syrupy mouthfeel. Much more bittersweet chocolate and clean roastiness. Slight acidic twang.
5) Cold brew (using a Cold Toddy brewer) - very little aroma and flavor. Almost no acidity and brightness. A very boring cup, even when drinking the straight concentrated brew. Watered back to the manufacturer's instructions absolutely killed it. This method also requires 1 full pound of grounds to make a relatively small volume of coffee.
6) Whole beans steeped in cold water for 1 week. Mild flavors and strong aroma. Not very dark.
As I mentioned before, the espresso is by far my preferred cup of coffee, ergo my preferred method for infusing coffee into beer on a homebrew scale.