Whisk together the sauce ingredients, then spoon out 1 1/2 tablespoons to coat the rinsed beef. Stir the cornstarch into the remaining sauce until smooth, then mix in the water.
Heat the peanut oil in a large nonstick pan or wok over high heat, then add the onion and garlic for 10 seconds. The oil should sizzle sharply and the garlic should smell fragrant without browning.
Add the coated beef and stir fry it quickly over the high heat. Move on when the strips change from deep red to light brown on the outside but are not cooked through.
Add the bell pepper, carrot, bok choy stems, and white green onion pieces, then stir fry for 1 minute. The vegetables should stay brightly colored, with carrots and stems retaining a crisp-tender snap.
Pour in the prepared sauce and stir continuously as it heats. Once the liquid bubbles, it will quickly become thicker and begin to cling to the beef and vegetables.
Add the bok choy leaves and green onion tops, then toss for 30 seconds to 1 minute. Stop when the leaves are just wilted and the sauce has a smooth, glossy sheen.
Serve immediately with steamed white rice and sesame seeds, if desired. The finished stir fry should be saucy enough to coat the rice without pooling thin liquid underneath.