It turns out to be possible to grow an entire farm on a 3-inch deep window sill. Spotted at Anthropologie:

Above: The Micro Greens Grow Box comes with seeds to grow organic red cabbage, mini carrots, and tom thumb peas. It's $40 from Anthropologie.

Above: The kit comes in a box made of recycled steel, and includes enough soilless growing medium and seeds for two full crops.