“We want to tap into the person who is like, ‘I just want to live my truth in my own weird, quirky way,’” said Sarah Tabb, the senior director of marketing, who spent six years as a brand manager for Coca-Cola.

Ms. Tosi plans to open Milk Bars in cities where there’s already a fan base, including Chicago and Miami. The company is upgrading its e-commerce, which is about a third of the business.

Then there is her holy grail: the grocery store. As someone with roots in central Ohio who grew up on hot dogs, Doritos and ranch dressing, she is a deep fan of packaged food, and the supermarket remains an inspirational touchstone. Milk Bar desserts on the shelves of America’s suburban grocery stores, she said, are her gift to children looking for creative inspiration in a sea of mass-market blandness.

But building an empire comes with a challenge familiar to many niche food entrepreneurs riding a growth spurt: “How do you do that,” she said, “without being like any other hockey-stick white dude?”

Ms. Tosi may be the unicorn that can, said Doug Quint, a founder of Big Gay Ice Cream, another only-in-New York brand that began just after Milk Bar and also is expanding.

“It takes a little time before you realize her genius,” he said. “It’s all so deep in her, she doesn’t even recognize it.”

One hurdle on her way up was changing her relationship with David Chang, the chef who first hired her to handle office business and later made her pastry chef for his Momofuku restaurants. He knew she wanted to open her own bakery, and gave her the seed money to do it.