Bring a pot of water to a boil and cook the brown rice according to package directions. Drain the rice and let it rest, covered with a lid. Meanwhile, rinse the bok choy and snow peas clean. Slice the white stems of the bok choy into thin strips and cut the green leaves into rough chunks. Keep the white and green parts separate. Peel the piece of ginger and grate it finely.
Heat a wok over high heat and let the pan get very hot. Add the sesame oil, immediately followed by the raw peeled shrimp and grated ginger. Stir-fry this mixture continuously for two minutes. Then add the snow peas and white bok choy strips to the wok. Toss everything and cook for three more minutes over high heat so the vegetables remain crispy and tender-crisp.
Add the reserved green bok choy leaves and soy sauce to the stir-fry. Toss the contents of the wok together immediately. Let the dish stay on the heat just long enough for the green leaves to wilt. Remove the pan from the heat to prevent the shrimp from becoming tough and the vegetables from overcooking.
Divide the warm brown rice among the plates. Spoon the shrimp stir-fry with the bok choy and snow peas on top of the rice. Pour any remaining liquid from the wok over the dish and serve immediately.