This recipe is from the wonderful, wonderful King Arthur Flour Whole Grain Baking cookbook. I have modified three ingredients and added some commentary; this is a pretty standard recipe. It will make plenty of frosting for 48 cupcakes.
Place the egg whites or the water and powdered whites in the bowl of your standing mixer. Place the corn syrup, sugar and water in a medium saucepan, stir until sugar dissolves, cover the pan and bring to a boil. Boil for 3 minutes, then uncover and cook to 245 degrees, which is right between soft-ball and hard-ball stages. There is some variation in recipes as to what temp the sugar syrup should be; 245 seems like a good compromise. A candy or instant-read thermometer is pretty vital for this; I have a high-end digital instant-read thermometer and use it all the time--it was a good investment.
While your syrup is cooking, begin to beat the egg whites on low speed. When they are foamy add the cream of tartar (for fresh whites) and salt. Gradually increase the speed and continue beating until soft peaks form. Then, slowly and CAREFULLY, pour the hot syrup directly into the middle of the whites. This isn't the way the recipe says to do it, but in my experience it works well as long as you have a thin enough stream of the syrup. Continue to beat for 20 minutes, or until the meringue is very thick and fluffy. It will almost certainly still be hot at this point. Remove the bowl from the mixer and place in a larger bowl of ice and water and let sit until completely cool, using a spatula to stir it up from the bottom a couple of times. Check the temp with your trusty instant-read thermometer and get it down to 70 degrees before proceeding. DON'T TRY TO HURRY THIS STEP! If you try to add the butter before the meringue is completely cool the butter will melt and you'll have a mess, as I said above, and you won't be able to rescue it.
Once the meringue is cool, start adding the butter and shortening bit by bit. It's worth the effort and an extra dirty bowl to beat the butter and shortening together before adding it to the meringue. Classic recipes for any kind of buttercream are made with all butter, but the small amount of vegetable shortening makes the buttercream more stable at warmer temperatures. As I said in the ingredients list above, I use Spectrum organic shortening, but, again, for this small amount Crisco probably wouldn't kill you. Believe me, this stuff tastes very buttery, even with the shortening added.
One big drawback of this recipe is that you really shouldn't make it ahead of time, although you can certainly make it and then frost the items ahead of time. But to make the buttercream and then refrigerate it separately and then bring it back to room temp, beating all the while, is kind of a process. Once your items are frosted, though, they can stay at cool room temperature overnight. I did some looking online and everyone seems to agree that frosted items don't have to be refrigerated unless it's going to be over two or three days--and why on earth would you do that?
If you make this with powdered egg whites then you can be completely sure that there's no salmonella involved. I'd never make this with fresh whites, myself, but I'm sure purists would faint dead away. I get absolutely great results with the powdered whites and the small amount of shortening. And I'm pretty much of a purist myself!
Here are a couple of variations to try, with more on the way:
Lemon:
Most recipes just tell you to beat in some lemon juice and zest at the end, but when I've done that I've felt that the texture of the frosting was compromised. So I suggest replacing half of the water in the sugar syrup with lemon juice (1/3 cup = 5 tablespoons + 1 tsp, or 16 tsp., so use 2 tablespoons + 2 tsp. water and 2 tablespoons + 2 tsp. lemon juice) and then beating in about 1/8 tsp. lemon oil with your butter/shortening mixture. The lemon oil won't affect the texture, and if it's still not lemony enough you can add more, but do so SPARINGLY, drop by drop. Citrus oils are EXTREMELY strong.
Chocolate:
Melt 2 oz. unsweetened chocolate and COOL. Beat in with your butter/shortening mixture so that you basically have chocolate butter, then beat that into the meringue.
I have some other variations I want to try and will add them here as I do so.