You can plant a garden of vegetables that grow above ground if the topsoil in your yard is shallow or rocky. These types of vegetables tend to have rather shallow root systems and will produce an adequate crop, especially if you help them out by feeding them regularly. Root vegetables, those that produce their crop beneath the surface of the soil, will not produce a satisfactory crop in shallow, rocky topsoil. The lack of depth and the presence of foreign objects cause their fruits to be stunted and misshapen.
Legumes (podded peas, green beans, chick peas and lentils) produce their crop from flowers produced on either vining or bush-like plants. Their tender, buttery flesh provides a complete protein source for humans when combined with a grain. Legumes also have the unique ability to take nitrogen from the air and secrete it through their roots, thereby enriching the soil.
Greens include spinach, mustard, collards and Swiss chard. Although they are most often eaten raw in salads along with lettuce, greens can also be cooked. The edible part of greens are the leaves, which are produced above ground. They prefer cool weather and are best planted in early spring and early fall.
Cole vegetables are members of a related family of vegetables, also known as "cruciferous vegetables." It is made up in part of broccoli, cauliflower, kale, Brussels sprouts and cabbage. The edible part of broccoli and cauliflower are actually unopened flower buds. On cabbage, Brussels sprouts and kale, the leaves form a tightly wrapped head---almost like a flower bud. All of these cole vegetables produce their crops on the above ground parts of their plants.