Brownie Pointss on Mount Street specialises in products like ice creams, luxury brownies, and iced teas.
Despite its unassuming location in a mainly industrial area of the city, Brownie Pointss has proved hugely popular, and videos of the desserts on offer have been viewed hundreds of thousands of times on social media platforms like TikTok.
The business has applied to Bradford Council for a licence to serve late-night refreshments until 3am.
Its current opening hours are listed online as 11am to midnight on Sunday to Thursday and 11am to 1am on Fridays and Saturdays.
A decision on the licence will be made later this summer.