You're right that 'any' can be used with a singular, countable noun to mean 'whichever [one]'. Your example doesn't quite work, though. With something as general as "I like cooking...", we'd probably say, "I like cooking all sorts of dishes". ' Any' presupposes some kind of limit, so when we use 'any' to mean 'whichever', we normally qualify it in some way. For example, "I like cooking any dish that's quick and easy". In a specific situation, you could say something like this: "I'll cook any dish you want."

Also you can say "Russa is larger than any other country in the world".