The vegetables that grow above ground include all types of legumes such as peas and green beans, all cole vegetables such as broccoli and cauliflower, and greens such as spinach and lettuce. These vegetables tend to have shallow roots, which allows them to be planted in rocky or shallow soil.
Legumes are normally found on bush-like plants and nourish the soil by releasing nitrogen from their roots. Similarly, the cole vegetables are grown on short shrubs and also include kale, cabbage and brussels sprouts. Typically if the edible part of the plant is the leaves or flowers, the vegetable is most likely grown above ground.