WHO would go to a restaurant to eat Frosted Flakes—and pay $6, maybe even $8 for it? What if the bowl was topped with a sprinkle of lemon zest, toasted pistachios and fresh thyme, and was singularly delicious?

Kellogg’s will find out the answer on July 4, when it opens its first-ever restaurant, in New York’s Times Square. The new Kellogg’s NYC will have none of the bling found in other Times Square outlets. Instead, Kellogg’s has partnered with Anthony Rudolf—former director of operations for chef Thomas Keller’s New York...