The inspiration behind the unusual burger wrap and video, he says, is Burger King's localized efforts to put into motion actions that support its recently-tweaked slogan: "Be Your Way."

"It showcases who we are as a brand," says Fernando Machado, senior vice president of global brand management at Burger King. "It shows how we, as a brand, believe in self expression."

Burger King on Wednesday morning at 8 AM EST plans to post a two-minute video about the Proud Whopper on its YouTube channel.

The Proud Whopper, as it's called, comes wrapped in a rainbow colored wrapper with this inscription: "We are all the same inside." It will be sold through Thursday at one Burger King restaurant on San Francisco's Market Street, that was at the heart of the route for last weekend's 44th annual San Francisco Pride Celebration & Parade.

has concocted yet another way to have it your way: a gay pride burger.

The move also demonstrates BK's desire to stay connected to its base of Millennial customers. Gay rights is an issue that reverberates strongly with many Millennials both inside and outside the U.S. Burger King also was a sponsor of San Francisco's gay pride parade. Machado says that's the first time Burger King has sponsored a gay pride parade in the U.S., though it may have sponsored some outside the country.

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The downtown San Francisco Burger King sold "Proud Whoppers" last weekend, during the parade and also passed out some 50,000 rainbow Burger King crowns, that were worn by parade participants and spectators. The video, created by the Miami office of Burger King's ad agency David, captures customers discussing whether or not the burger, itself, is different. At $4.29 it costs the same as a conventional Whopper. And, indeed, customers ultimately discover the only difference is the rainbow wrap.

All Proud Whopper sandwich sales, Machado says, will be donated to the Burger King McLamore Foundation for scholarships benefiting LGBT high school seniors graduating in spring 2015.

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One gay rights activist says BK is doing the right thing. "Whenever a company comes out in support of gay people, it makes a difference," says Jordan Bach, a consultant to corporations on gay rights issues and a GLAAD media partner. "But when it's done right—when it's done with a campaign that shows the company understands diversity and really believes in the profound acceptance of other people—that sort of marketing can change minds and hearts at the deepest level."

For the moment, Burger King has no plans to broaden the promotion, Machado says, but notes, "we may consider something even bigger later on."

As for the wrappers, he says, they've already become collectibles. "Customers were folding the wrappers and taking them home with them," he says. Pretty soon, he says, they'll probably show up on eBay.