An easy way to get a start is by converting your Curl command to a Perl program using (my) Curl to Perl converter:
my $ua = LWP::UserAgent->new( 'send_te' => '0' );
my $r = HTTP::Request->new(
'GET' => 'https://example.com/',
'Accept' => '*/*',
'User-Agent' => 'curl/7.55.1',
'Cookie' => 'session=536...035a'
my $res = $ua->request( $r, ':content_file' => 'HTML_output.txt' );
Created from curl command line
curl https://example.com --cookie "session=536...035a" -o "HTML_output
I'm not sure if your Firefox stores its cookies in a cookies.txt file still or if it stores them in an SQLite database nowadays.