Why did my ice cream turn out like this? I suppose I should mention that its texture came out PERFECTLY, and I'd really like it to do this again.

The first thing I did was heat 2 cups of sugar and 3 cups of half and half over low-ish heat, with some vanilla bean paste. Then, I tempered 9 heavily-whisked egg yolks with some of the half and half mixture. I added 3 T of Skyy vanilla vodka, forgetting that I was supposed to do that during the mixing process, not the custard-ing one. It curdled slightly, so I blended it, heated it gently again, and then strained it with a fine wire mesh strainer. I refrigerated it for several hours, forgetting to add the 3 cups of cream specified in the instructions.

Well. Not forgetting. I thought I was supposed to do it later, because evidently I don't read instructions effectively.

So then I took it out of the fridge. It was lovely and thick. I added the cream that I was supposed to have added earlier, didn't add more of the vodka I was supposed to have added at this point, and ended up with a very thin ice cream mixture. Pretty much liquid. I added a little salt, beat it in a very, very frozen ice cream mixer bowl (KitchenAid) (VERY frozen) for thirty minutes. It became slightly thicker, like a milkshake that forgot to be thick and was mostly melted. I drizzled in a little homemade caramel (1 cup sugar, 3/4 cup cream, a little vanilla, some salt). It then froze over night. I took it out of the freezer. The texture was PERFECT. Very scoopable, no ice crystals, didn't get overly hard, and the taste was spectacular.

Is the beautiful texture because I put in the cream later? Because I added the vodka? Because the ice cream gods decided they liked me last night? What in that set of steps resulted in that texture, so I can repeat this with recipes that aren't that one, not intentionally making 'mistakes' that I might not have to make so it comes out this way again?
Why do you think it was one single thing you did? It turned out good because the whole process was within the parameters which produce a good ice cream. A single mistake can ruing an ice cream, but a single right thing cannot make an ice cream. 


  so I can repeat this with recipes that aren't that one, not intentionally making 'mistakes' 


If a good recipe is followed correctly, it will turn out this way without the need to do anything else. An ice cream which gives bad results means that either the recipe was not good enough, or that you made a (real) mistake somewhere while making it. 

There are no magic tricks in making ice cream, some little thing which turns any strange mass into a fluffy wonder. There is expertise, and knowing why each step is done a certain way. Once you know this, you will be able to fix bad recipes by correcting whatever is missing. But this knowledge is too much to fit this paragraph. Basically, you need to internalize some simple ideas of food chemistry (such as fat globules getting in the way of proteins trying to coagulate), then learn the basics of egg chemistry and custards, and then learn about ice cream and freezing. Reading the chapters on eggs and dairy from McGee on Food and cooking should be sufficient. But we cannot write up these couple of hundred pages here in an answer. 

You can also read our other questions on crystalizing ice cream, they have short guidelines. I found this one with a quick search, but there are more. The Perfect Scoop also starts with a chapter explaining some of the methodology behind ice cream, before starting with recipes. These are good ways to start, and may be sufficient for you. They won't be enough for learning how to create your own recipes, or even for recognizing problematic recipes before making them. But once a recipe has failed, they give you a few options of what to try with the hope that it can be made to work next time.