You could use a HoL:

(Disclaimer: probably not the most optimal solution :)

#!/usr/bin/perl -w
use strict;

my %data;
my $header;

while (<DATA>) {
    chomp;
    if (/Usr/) {
        $header = $_;
        next;
    }
    my ($timestamp, $rest) = $_ =~ /(\d{2}-\d{2}-\d{4}:\d{2})\s+(.*)/;
    push @{ $data{$header}{$timestamp} }, $rest;
}


foreach $header (keys %data) {
    foreach my $timestamp (keys %{$data{$header}}) {
       print "$header\n";
       print "$timestamp\t$_\n" for @{$data{$header}{$timestamp}};
    }
}

__DATA__
   Usr1369***12556
06-01-0101:00    1169 <snipped off>
06-01-0101:00    2396 <snipped off>
06-01-0103:12    1169 <snipped off>
06-01-0103:12    2569 <snipped off>
06-01-0301:00    1169 <snipped off>
06-01-0301:00    2396 <snipped off>
[download]

Output:

   Usr1369***12556
06-01-0103:12   1169 <snipped off>
06-01-0103:12   2569 <snipped off>
   Usr1369***12556
06-01-0101:00   1169 <snipped off>
06-01-0101:00   2396 <snipped off>
   Usr1369***12556
06-01-0301:00   1169 <snipped off>
06-01-0301:00   2396 <snipped off>
[download]

Cheers,
Darren :)