The project evolved after a producer heard Broussard's contribution to "Oh Say Can You Sing?" -- the compilation CD featuring the musical talents of players such as teammate Coco Crisp and Omar Vizquel of the San Francisco Giants.
Broussard's rendition of U2's "With or Without You" prompted the producer to ask for some original material.
"I sent him a couple bootleg copies of me just taping myself, and he was like, 'This is really good. We ought to get in the studio,'" said Broussard, wearing flip-flops, cargo shorts and a white Indians jersey.
Broussard, batting .255 with nine home runs and 36 RBIs, recorded the material while on break from baseball.
"In the offseason, I met up with him in the studio and I just laid down all the vocals, all the guitar that I could, and then got some [people] to play drum and bass," Broussard said. "And now the CD is being mixed."
Broussard said he began strumming the guitar in eighth or ninth grade and continued the hobby at McNeese State University in Louisiana, where he played in a cover band and rewrote the school's baseball record book.
Traveling during a 162-game schedule helps Broussard work on his songwriting.
"When I'm on the road, you know, I got lots of time -- just kind of a way for me to unwind after games," said Broussard, who also performed on Monday night at a Major League Baseball party outside Comerica Park.
Before walking out to perform in front of a small crowd gathered at FanFest's replica baseball field, Broussard listed Pearl Jam, Ben Harper and Radiohead as some of his favorite bands.
Broussard indicated the reaction in Cleveland's clubhouse has been generally positive, as most of his closer friends have already heard the songs.
"Some guys give me a hard time a little bit about it ... but they get used to it. They know who I am and what I'm about," Broussard said.