Adjust racks to top and middle positions and preheat oven to 425˚F. Wash and dry all produce. Peel and mince ginger. Trim and thinly slice scallions, separating whites from greens; mince whites. Prepare beans, cutting off ends, if necessary. Quarter lime.
Melt 2 tablespoon butter in a small pot over medium-high heat. Add half the ginger and cook until fragrant, 30 seconds. Add rice, 1½ cups water, and a big pinch of salt. Bring to a boil, then cover and reduce heat to low. Cook until rice is tender, 15-18 minutes. Keep covered off heat until ready to serve.
While rice cooks, in a large bowl, combine beef, scallion whites, panko, remaining ginger, salt (we used 1¼ tsp kosher salt), and pepper. Gently combine, then form into four 1-inch-tall loaves. Spread out across entire baking sheet.
Add green beans to a second baking sheet and drizzle with oil; roast meatloaves on top rack and beans on middle rack. Roast until meatloaves are cooked through and broccoli is browned and tender, 15-18 minutes.
Meanwhile, in a small bowl, combine sweet soy glaze, ketchup, a pinch of chili flakes to taste, and a squeeze of lime juice to taste. In the last 2-3 minutes of roasting, remove meatloaves from oven; brush tops with 1 tablespoon glaze mixture on each. Return to oven until glaze is tacky. TIP: Save any remaining glaze mixture for serving.
Fluff rice with a fork and season with salt and pepper. Toss beans with ponzu sauce and half the sesame seeds. Divide rice, beans, and meatloaves between plates. Drizzle meatloaves with any remaining glaze mixture. Garnish with scallion greens, remaining sesame seeds, and as many chili flakes as you like. Serve with remaining lime wedges on the side.