#!/usr/bin/perl -l
use strict;
use warnings;

my $file;
{
  local $/ = undef;
  $file = scalar <DATA>;
}

## Find me two newlines or be the start of the file
## Followed by any amount of newlines
## Followed by one or more characters (our capture, your paragraph)
## Followed by any amount of newlines
## Followed by any two newlines or the end of the file
## Flags: treat the file as one line, continue search for more paragraphs (/g in list context)
while ( $file =~ m/ (?>\n{2}|\A) \n* (.+?) \n* (?=\n{2}|\z)/sxg ) {
  print "<p>$1</p>";
}

__DATA__

Paragraph one is this

Paragraph two is this


Paragraph three is this
Paragraph three and this
But stops here and doesn't get the rest of the newlines