Davidoff draws from a new source for one of its latest releases, the Escurio.

After leaving Cuba in 1989—when company patriarch Zino Davidoff publicly burned more than 100,000 Cuban cigars that he deemed unfit to sell—the Switzerland-based brand Davidoff was associated only with cigars from the Dominican Republic. Then in 2013 it introduced its first Nicaraguan puros. (The Davidoff Nicaragua Diadema, launched in 2014, was a Robb Report Best of the Best selection last year.) Now the cigar maker has stretched…