This one does both parts (along with creating the initial file).

It uses module Path::Tiny - if you don't have it, install it from CPAN.

#!/usr/bin/perl

# http://perlmonks.org/?node_id=1193831

use strict;
use warnings;
use Path::Tiny;

my $dir = 'folder';
my $input = 'bigfile.txt';
my $output = 'rebuiltfile.txt';

################## create (fake) big file ##################

path($dir)->mkpath;
path("$dir/$input")->spew( map "line $_\n", 1..11 );

#################### split to 2 lines per file #############

my @lines = path("$dir/$input")->lines;
my $number = () = glob "$dir/*";
path("$dir/bladibla_" . $number++ . '.txt')->spew(splice @lines, 0, 2)
  while @lines;

#################### combine ###############################

path("$dir/$output")->spew(
  map $_->[0]->lines,
  sort {$a->[1] <=> $b->[1]}
  map [ $_, "$_" =~ /(\d+)/ ],
  path($dir)->children( qr/^bladibla_\d+.txt$/ ));
[download]