In-Stock and Ready To Ship Today! – Big Papi David Ortiz Cigars: Official Cigars of the Red Sox Baseball Legend David Ortiz. Looking for the official Big Papi David Ortiz cigars? You have come to the right place. HOLYSMOKESCIGARS.COM was one of the first to introduce the Big Papi cigars. Made by one of the most famous cigar makers in the world “El Artista Cigars” based out of the Dominican Republic.