Broccoli is an edible vegetable originating from the planet Earth. It was among the foods served about Earth Starfleet vessels during the 22nd century.
While stranded in the desert region of the Torothan homeworld, Captain Archer promised a hungry Trip Tucker that he would have Chef prepare an unforgettable dinner and then, to keep his chief engineer conscious, asked him what he would like to eat. Besides prime rib and mashed potatoes, Trip requested that his meal also include broccoli. (ENT: "Desert Crossing")
In 2152, while waiting a neutronic storm in the ship's catwalk, Travis, Hoshi and Malcolm played a game of cards, using their ration packs as bargaining chips. Among the rations being played was broccoli, but it was only included after Hoshi ran out of desserts. (ENT: "The Catwalk")
"Broccoli" was a nickname that Wesley Crusher applied to Reginald Barclay. It began as a form of inside joke at the expense of Barclay due to his perceived ineptness and nervousness. (TNG: "Hollow Pursuits")