Jim Parsons says he has had "an awakening" of how much he loves "bringing myself to the work" in portraying LGTBQ+ characters in recent years.

In an interview with Variety for the outlet's Just for Variety podcast Wednesday, Parsons, 49, noted that "the majority" of roles he is offered are gay characters.

"I wouldn't necessarily call it a lot of LGBTQ+ content, but there are a lot of gay characters that I get offered," Parsons said when asked what kind of scripts he's sent. "The majority, I would say, that I get offered are gay."

"I think that a decade ago, if you'd have told me I'd be an out actor, and that I would therefore get offered tons and tons of gay roles, I'd have been like, 'Well, that seems like an easy, tired thing to have happen,' ' he added.

In recent years, Parsons — who quietly came out as gay via a 2012 profile in The New York Times — has played gay characters in HBO's 2014 movie The Normal Heart, 2020's The Boys in the Band and the miniseries Hollywood, in addition to his new role in Spoiler Alert.

Jim Parsons Tackles Love and Loss in Touching Trailer for Film Adaptation of Spoiler Alert

"They have been such rich characters and in such interesting storylines that I have had an awakening of how much I love as an actor — and, if I may say, artist — bringing myself to the work," Parsons said of these roles.

Elsewhere during the interview, Parsons noted that he "grew up in a time where the first thing I think of every time" on the topic of being openly gay in Hollywood "is when Ellen [DeGeneres] game out."

"It was so exciting. As much as it helped ultimately, it was also f------ scary as a gay person who wanted…a career for themselves, in the same road, in the same industry," the actor added. "So, it's been a long time coming."

Never miss a story — sign up for PEOPLE's free daily newsletter to stay up-to-date on the best of what PEOPLE has to offer, from juicy celebrity news to compelling human interest stories.

Spoiler Alert, which stars Parsons and Ben Aldridge, is an adaptation of Michael Ausiello's heartfelt and critically acclaimed memoir Spoiler Alert: The Hero Dies.

The film tells the true story of Ausiello's (Parsons) 13-year relationship with photographer Kit Cowan (Aldridge), who died in February 2015 at the age of 43 after an an 11-month battle with a rare and brutal form of cancer.

The Biggest Revelations from The Big Bang Theory Oral History Book

The movie comes from director Michael Showalter (Wet Hot American Summer, The Big Sick, The Eyes of Tammy Faye). Sally Field and Tony winner Bill Irwin appear in the film as Cowan's parents, while Jeffery Self, Tony winner Nikki M. James, Tara Summers, Paco Lozano, and Queer Eye's Antoni Porowski also star.

Spoiler Alert hits theaters in New York, Los Angeles and San Francisco on Dec. 2, ahead of a Dec. 9 domestic open. A worldwide release is scheduled for Dec. 16.