Wash and dry all produce. Bring 2 cups water to a boil in a small pot. Trim bottom root ends from bok choy and discard. Cut head in half lengthwise, then slice crosswise into strips. Trim, then thinly slice scallions, keeping greens and whites separate. Peel, then mince ginger until you have 2 TBSP. Mince garlic.
Once water is boiling, add rice to pot. Cover, lower heat, and reduce to a simmer. Cook until tender, 15-20 minutes. Remove from heat and keep covered until rest of meal is ready.
Combine soy sauce, hoisin sauce, honey, half the ginger, and half the garlic in a medium bowl. Add beef and toss to coat. TIP: If you have extra time, let beef marinate for up to 3 hours in the refrigerator.
Heat a drizzle of oil in a large pan over medium-high heat. Add beef to pan, leaving excess marinade in bowl. Cook, tossing occasionally, until browned and almost cooked through, 2-3 minutes. Remove from pan and set aside.
Add scallion whites, remaining ginger, remaining garlic, and another drizzle of oil to same pan over medium heat. Cook, tossing, until fragrant, about 1 minute. Add bok choy and cook, tossing, until tender, 3-4 minutes. Season with salt and pepper. Return beef to pan along with marinade from bowl. Let bubble until a thick sauce has formed, 2-3 minutes. Season with salt and pepper.
Divide rice between plates. Top with stir-fry. Sprinkle with scallion greens and sesame seeds and serve.