Plastic towers are scattered across the flat roof with cups on their side which hold the plants. 20 gallon water tanks anchor them at the base, and also provide a nutrient-rich solution for the plants. Every 12 minutes warmed water is pumped up the tower and then trickles down for three minutes past the roots, which are held in rockwool balls. As the water is recycled, only 10% of the water needed for lettuces, for example, is needed. The pump motor is very economical as well. The towers can be 9 feet high (but are lower in this case as the building facade is listed and they must not be viewed from the street).
The plants also grow much faster than normal. All the restaurant's needs are met for four months of the year, and about a third is provided in all except the two coldest months. However, the food cannot be certified organic because US regulations say that the majority of fertilisers have to come from plants and animals, while the system uses mineral sources. Still, food miles are definitely minimised.
The article states that Tim Blank, the CEO and founder of Future Growing, came up with this Tower Garden system in 2004. It is an interesting variant on the vertical gardens movement, and the general idea is called aeroponics as a variant on the established hydroponics idea.
I couldn't find any published patent specifications under the company name or that of Blank, but have come across a rather similar invention by Robert Simmons of Florida, applied for in 2009 as Apparatus for aeroponically growing and developing plants. The main drawing is given below.