I strongly advice against using the same subs for different APIs.*

If you really want to go with this strange requirement - what is $self supposed to be in non method calls (?) - you can use a different namespaces to mirror the function/methods.

 
# UNTESTED
package functional_Util;
my $default_self= "something";
sub utility {
   unshift $default_self, @_;
   goto &methodlike_Util::utility;
}

package methodlike_Util;
sub utility {
   my $self =shift;
   # ... do it
}
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Of course you are free to use it the other way round if $self doesn't matter.

Please note that Perl is flexible enough to autogenerate the needed "mirrors", either/or per

• AUTOLOAD
• inside an import routine
• a BEGIN Block

It's a trade: You are gaining large runtime performance and a clean interface for adding little compile-time complexity.

But again I doubt the requirements are well thought off, sounds like a political compromise inside a big team meeting where everyone wants his own private menu in a restaurant just to prove he knows cooking.

update

*) since checking the arguments is complicated, error prone and slow, see other replies.