This is reminiscent of a common trick in (untyped) lambda calculus to make a function recursive -- called a Y combinator.

In fact, using a standard Y combinator, you don't have to change the public interface to the function -- you use currying to fix the extra parameter that is introduced:

my $func = sub {
    my ($call_next, $param1, $param2) = @_;
    do { something };
    $call_next->($call_next, $newparam1, $newparam2);
};

my $nice_func = sub { $func->($func, @_) };

## now you don't have a bizarre calling convention:
$nice_func->(param1, param2);
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I also like this better than your example because it doesn't use the $func variable confusingly in 2 different scopes (when I saw your original code, I had to think hard about whether you introduced a cyclic reference for $func).

Update: I should add that this won't result in a cyclic reference like the approaches in the previous replies.

See also: Re: recursive anonymous subroutines and this entry from Aristotle's use.perl journal.