What is the best way...

Perhaps something using Date::Calc. The idea would be to take a date in the year, find the next monday, and if the year is the same, print it out. Then, keep adding 7 days until the year changes.

#! /usr/bin/perl

use strict;
use warnings;

use Date::Calc 'Add_Delta_Days';

my ($day, $month, $year, $dow) = (localtime)[3, 4, 5, 6];
$year  += 1900;
$month += 1;

my $this_year = $year;
($year, $month, $day) = Add_Delta_Days($year, $month, $day, (8 - $dow)
+ % 7);

while ($this_year == $year) {
    printf "%04d-%02d-%02d\n", $year, $month, $day;
    ($year, $month, $day) = Add_Delta_Days($year, $month, $day, 7);
}
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update: it occurs to me that it may not be obvious how this calculates Mondays, since it uses a magic number. It would be a little clearer had I written:

my %day = qw(
  Sun 0
  Mon 1
  Tue 2
  Wed 3
  Thu 4
  Fri 5
  Sat 6
);

($year, $month, $day) = Add_Delta_Days($year, $month, $day, (7 + $day{
+Mon} - $dow) % 7);
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