The new shop, on what they refer to as “the campus,” will be connected to the restaurant and wine bar by a single kitchen whose warrens full of olives, wine and dough weave behind and under the restaurants.

“The pizza project is the pizza project: You’re in and you’re out,” Mr. Castronovo said. “You’re not getting wined and dined. We have a restaurant for that, and we have a wine bar for that.” (Their Frankies Spuntino Group also includes Frankies 570 restaurant in the West Village.)

When they started talking about opening a slice shop last year, around the same time they opened their wine bar, they turned to the acclaimed pizzaiolo Umberto Corteo, who has owned his Long Island shop, Umberto’s, in New Hyde Park, N.Y., since 1965. That deal fell through, but both Mr. Corteo and the Franks say they are still friends.

“We grew up eating his pizza as kids,” Mr. Falcinelli said. “He’s kind of like the pizza king.”

All the same, the Franks bought the small building on Court Street where they will open their pizza shop. They had originally planned to open it in Cobble Hill, where they ran a coffee shop, Cafe Pedlar, until it closed in 2017. But when the building between their two restaurants became available, they couldn’t pass it up. They also knew they didn’t want to use the machine-made commercial ingredients common to most New York slice shops.

“They put bromine in the flour,” Mr. Falcinelli said. “It preserves it, it gives it that New York texture, but it burns. It’s basically fake dough conditioner.”

The new shop will use Mr. Robertson’s approach to making dough, with grain freshly milled every two weeks, well-hydrated dough, gentle mixing and a long rise with a natural sourdough leaven.