use Net::DNS::Resolver::Base;
  my $orig= \&Net::DNS::Resolver::Base::nameservers;
  local *Net::DNS::Resolver::Base::nameservers= sub {
    my ($self, @servers)= @_;
    print "Current nameservers value: "
      .join(", ", @{$self->{nameservers}//[]})
      ."\n";
    print "Assigning nameservers: ".join(", ", @servers)."\n"
      if @servers > 1;
    $orig->(@_);
  };

  # and then the rest of your program