<p>I've been trying this a few different ways, but I'm reaching the conclusion that it can't be done. It's a language feature I've enjoyed from other languages in the past. Is it just something I should just write off?</p>

No, static indexers aren't supported in C#. Unlike other answers, however, I see how there could easily be point in having them. Consider:
```
```
Encoding x = Encoding[28591]; // Equivalent to Encoding.GetEncoding(28591)
Encoding y = Encoding["Foo"]; // Equivalent to Encoding.GetEncoding("Foo")
```
```
It would be relatively rarely used, I suspect, but I think it's odd that it's prohibited - it gives asymmetry for no particular reason as far as I can see.