The rapidly expanding Shake Shack franchise will open its second Brooklyn outpost next month at 1 Old Fulton Street in Dumbo. Community Board 2’s transportation committee approved a small sidewalk cafe last week for the burger joint’s new storefront, which sits on the corner of Water and Old Fulton Streets facing Brooklyn Bridge Park. The cafe will have four tables with eight seats on the Old Fulton Street side of the building, where Shake Shack recently put up signage. The manager told us that he hopes to open in the next few weeks. The spot’s former occupant was Pete’s Downtown restaurant, which began serving Italian food in the early ’80s and closed in December 2011.