"In the Greek style." This usually refers to vegetables stewed with oil, often with coriander (US: cilantro) seeds and generally served after they have cooled to room temperature.
With a dressing of lemon juice and olive oil, usually of green vegetables such as asparagus, catalogna, spinach or broccoli, sautéed and cooled. The resulting flavour should be quite sharp.
"In the style of Grossetana." A dish from Tuscany of pasta with a sauce of mushrooms and tomatoes, served with grated cheese.