Here in dry Reno NV, I have been able to harvest garlic chives, yucca root, garlic, pine nuts, dandelion greens, and tatsoi with zero irrigation in drought years.
For the tatsoi, I dug oval shaped "bowls" with graduated sides in clay soil about 8 inches deep by 2 feet long by one feet wide. I filled the hole with "fluffy" dirt (1 part compost, 1 part aged manure, 1 part peat moss). When the rare rain forecast arrived, I sprinkled tatsoi seeds and then lightly patted a little fluffy dirt on top. The tatsoi matured faster than it's water supply evaporated. I have a strong hunch that this would work with other fast growing veggies. (Radish? Lettuce? Spinach?) The trick is to have a non-permeable soil "bowl" ready and move fast when the sky gets that extra bit of color in it.
I know you want to know only about vegetables, but in the desert every trick in the book must be used;vegetables, fruits, shrubs, herbs, and trees rely on each other. Beside those "bowls" of tatsoi were other non-vegetable edibles that didn't leach away the tatsoi's water, and kept them relatively shaded from evaporation. Other climates may have the luxury of segregating vegetables into their own separate geography, but we do not.
