Now, the first thing we need to clear up is that this is NOT a recipe for a rolled fondant. This is not the sort of fondant that you would find in a thick white (generally inedible) layer on the outside of a wedding cake. The texture of this is more like the chocolate topping on doughnuts . . . something that isn't quite icing and is smooth and rather firm. It's fabulous stuff, and because it is just sugar, water, and corn syrup it stores quite well at room temperature for a long time. Some of the YouTube videos I watched said it was good for several months. I don't know for sure that that is true because the longest a double batch has survived my B&W cookie making binges is 2 weeks. But it was still fabulous after two weeks, for what that's worth.
The second thing that you should know is that it takes a little practice to get this right. Well, it took some practice for ME to get this right. Hopefully the things that I have learned over the last few weeks will make your learning curve less steep than mine. But the point is, don't give up if it doesn't turn out quite right the first time. It's totally worth the effort.
2 1/2 c. sugar
1/2 c. water
1/4 c. corn syrup
Combine all ingredients in a heavy saucepan. (I generally use my pressure cooker because it cooks evenly with no hot spots.) Cook over medium high heat until it boils, stirring gently the whole time. (Try not to splash up on the sides of the pan. Sugar crystals that don't get thoroughly dissolved into the syrup will cause problems with your fondant. Any undissolved crystals that remain in the final syrup will quickly cause the rest of the syrup to re-crystallize . . . thus undoing all your hard work.)
Once the syrup has come to a rolling boil, decrease the heat to medium, attach a candy thermometer to the side of the pan, and stop stirring. Use a pastry brush or a very wet paper towel to wash any stray sugar crystals down from the side of the pan. Let the syrup boil until it reaches 238 degrees.** (**Remember that, when cooking candies, you must decrease the temperature by 2 degrees Fahrenheit for every 1,000 feet above sea level. Here in Utah County I only cook this syrup to 228 degrees.)
Once the syrup reaches 238 degrees, remove it from the heat and pour it into the bowl of a stand mixer. DON'T scrape the sides or bottom of your pan, as that will create crystals that will re-crystallize the rest of your syrup. Clean your candy thermometer and then insert it into the syrup again. Allow the syrup to cool to 140 degrees. (This takes 30 - 50 minutes, but it's really important. If you try to move on without allowing the syrup to cool you will end up with little rocks of sugary stuff and then you will be unhappy. I think it does that because all the moisture steams out of it so quickly when it is that hot. One of these days I'm going to try letting the syrup cool on a cookie sheet and then transfer it into my mixer because I'm sure it will cool faster and I'm always really impatient . . . but I haven't done it yet and so I can't guarantee that it will work.)
Once the syrup has cooled to 140 degrees, turn on the mixer. (I use a K beater attachment for this). The syrup will first turn yellow and then white. As soon as it turns white, pour it into a ziploc bag that you have stretched open over a glass measuring cup or something. (Don't beat it too long after it turns white as it will harden very quickly and then your mixer might seize up and you will be unhappy again. It really only takes a couple of minutes to turn white, so don't walk away from your mixer while you are doing this.) If it gets rather firm while you are removing the beater, just scrape it out of the mixer bowl with a wooden spoon . . . it should be okay.
Seal the fondant air-tightly and store at room temperature.
Vanilla Poured Fondant - Make a simple sugar syrup by bringing 4 Tbs. sugar and 2 Tbs. water just to a boil. Remove from heat. Place between 1/2 c. and 1 c. of fondant in a double boiler*. (*I make a pseudo double boiler by putting 1 1/2 cups of really hot water in my 4 cup glass measuring cup, then placing my 2 cup glass measuring cup inside it.) Add a Tbs or so of the simple syrup to the fondant and stir it with a spoon until smooth, adding more simple syrup as necessary. (You'll have to rather chop at the fondant at first, but it will thin down and become easier to stir soon.) If you add too much syrup, the only way to fix it is by adding more fondant, so be careful not to overdo it. Once the fondant is smooth and spreadable, add about 1/2 tsp. vanilla.
Chocolate Poured Fondant - Add a couple of Tbs. of dutch processed cocoa to your vanilla fondant. Stir well. Add more simple syrup as needed to make it spreadable.
If you need more information on Poured Fondant (or want to see some pictures), this blog post by Joe Pastry is very helpful. I also found some great information at this site, although I don't agree with some of the information provided there (I've tried cooking it quickly and it always seemed to crystallize into a thick crust almost as soon as I poured it out of my pan).