Basche was born in Hartford, Connecticut. His first acting role was in a school production of The Adventures of Tom Sawyer when he was in the sixth grade at West Hartford's Norfeldt Elementary School. Basche, who describes his demeanor then as an "angry, smart-ass kid," tried out for and landed the lead role after a school counselor suggested he take up acting to channel some of his anger and emotion. Basche appeared in several plays presented by the Greater Hartford Jewish Community Center while he was a student at King Philip Middle School, and he had roles in 10 school plays during his four years at William H. Hall High School in West Hartford. Basche then went on to Emerson College, starting out as a communications major before switching to performing arts.