The Boston Licensing Board yesterday approved plans by Insomnia Cookies to open a warm-cookie storefront on Bromfield Street that would be open until 3 a.m. to serve downtown college students and long-term residents looking for a break from pizza and Chinese food in the witching hour.

The chain, which already has outlets in Kenmore and Harvard Square, says that while the store will be open until 3, it will accept its last order for warm-cookie delivery at 2:45 a.m.

Although the mayor's office and City Councilor Ed Flynn had supported making Boston a bit less of a city that rolls up its sidewalks earlier than most world-class cities, the Downtown Boston Business Improvement District had asked the board to let the cookies crumble at 2 a.m.