This sounds like basic inheritance.

package Parent;

sub new {
  my ($class, @args) = @_;
  bless [ @args ], $class;
}


package Child;

@ISA = 'Parent';
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Calling Child->new will call Parent's new() method, but $class will be 'Child', not 'Parent'.

The "trick" is using the first argument to the class method as the class name, not hardcoding the class name into your code.