Java8: HashMap to HashMap using Stream / Map-Reduce / Collector

I know how to “transform” a simple Java List from Y -> Z, i.e.:

List<String> x;
List<Integer> y = x.stream()
        .map(s -> Integer.parseInt(s))
        .collect(Collectors.toList());

Now I’d like to do basically the same with a Map, i.e.:

INPUT:
{
  "key1" -> "41",    // "41" and "42"
  "key2" -> "42"      // are Strings
}

OUTPUT:
{
  "key1" -> 41,      // 41 and 42
  "key2" -> 42       // are Integers
}

The solution should not be limited to String -> Integer. Just like in the List example above, I’d like to call any method (or constructor).