I looove frosting. I'm the one at the birthday party who wants the corner piece with all the roses piled on top and I'm not afraid to admit that when I'm done making frosting, I eat the scraps out of the bowl.
The world of frosting is big and beautiful- there are hard royal icings, cooked fudge frosting, marshmallowy meringue frostings, glazes, ganaches, and of course, buttercreams. Buttercream is probably the most popular frosting (in America, at least), but there are so many varieties...
My personal favorite is simple buttercream(sometimes referred to as "American" buttercream.) It's easy to make, is uncooked and pipes like a dream. It is, however, so sugary it makes your teeth burn. Most bakery "birthday" cakes- the kind with roses- are iced with simple buttercream. It's also what I used in my yo-yo cookies- you can find that recipe here.
Simple buttercream is made by creaming a fat with confectioner's sugar and flavorings. For the fat you can use butter, shortening or a 50/50 of the two. All butter tastes the best, but doesn't pipe as well because the butter gets soft at room temperature, also, the icing is a little ivory in color. All shortening tastes the most "fake", but pipes the best, is pure white and holds its shape best if it's a little warm. I like a half-and-half of butter and shortening, as you get the nice buttery flavor, but also the stability of the shortening. I also add an egg white to mine. It may sound gross, but the egg white really helps give the frosting a nice, smooth mouth feel. You can leave it out and use a tablespoon or two of cream, but the frosting is a little grittier. They sell pasteurized egg whites in a carton, as well as pasteurized in-the-shell eggs if you don't want to take your chances with food borne illness.
If you want something that's a little less dense and a little less sweet,but that still pipes well, Italian buttercream is a pretty good choice. It's a little more complex, as it has a cooked meringue base, but it is much less sugary tasting. It pipes quite well, and I like it better on very sweet cakes. (Sorry, this is a by-weight recipe...if you don't own a food scale, I highly recommend them. Not only does it make European recipes a cinch, but baking is so much less messy when you weigh it. They're only about $20. It's a good investment.)
4oz egg whites
10oz butter, room temp.
1tsp vanilla extract
In a heavy bottomed saucepan heat sugar and water until they reach 240F. While the sugar is heating, put your egg whites in your mixing bowl. When the sugar is at about 200ish, start whipping the egg whites to med-stiff peaks. Once sugar reaches 240F, reduce the speed on the egg whites to low and slowly and carefully whip the hot sugar into the whites. Once all the sugar is in, add the vanilla and turn up the speed and whip the mixture until it is cool. (No warmer than body temperature!) Turn the speed down, and add the butter in chunks, waiting until one chunk is incorporated to add the next. Once the butter is all in, whip a little longer, until fluffy.
(Be sure your meringue is pretty cool before adding the butter, or it'll just melt and make buttery sugar soup.)
French buttercream is similar in preparation to Italian buttercream, but is made with yolks instead of whites. It's very rich, but just lightly sweet. It's pretty soft, and doesn't really pipe that well. You could get a border and some filigree out of it, but not roses. It's very delicious, though.
3oz egg yolks
10oz butter, room temp.
The preparation is basically the same as for Italian buttercream, so I'll give you abridged directions. Whip the yolks until they are light and thick. Cook the sugar and water to 240F. With the mixer on low, slowly drizzle the sugar into the yolks. Add the vanilla, and whip until cool. Add the butter in small chunks while still whipping. Whip until fluffy.
Last, and definitely least (in my opinion) is Swiss buttercream. It pipes really well, but tastes exactly like the "honey whipped margarine" that they put in little paper cups on breakfast buffets. Seriously, it tastes primarily of butter, and then, as a faint aftertaste, a tiny bit of sweetness. I love frosting, but Swiss buttercream is where I draw the line. I'm telling you about it, so you are aware of its existence, but I'm not going to post a recipe. I can't in good conscience inflict it on others. If you're really passionate about eating butter, you can scour the internet and find a recipe yourself.
Hopefully, these recipes are helpful, and will provide you with a bit of direction in the vast and varied land of frosting options. Don't be intimidated by the cooked frostings, because the flavor and textures are truly divine, and really, they aren't that hard to make. Happy frosting, my friends!