Adjust rack to top position and preheat oven to 425 degrees. Wash and dry all produce. Trim, peel, and cut carrots on a diagonal into 1/2-inch-thick pieces. Peel and mince or grate ginger. Trim and thinly slice scallions on a diagonal, separating whites from greens.

Toss carrots on a baking sheet with a drizzle of olive oil, half the ginger, salt, and pepper. Roast on top rack until tender and lightly browned at the edges, 20-25 minutes.

Meanwhile, melt 1 TBSP butter in a small pot over medium-high heat. Add half the sesame seeds and cook, stirring, until golden brown, 2-3 minutes. Add rice, scallion whites, 3/4 cup water (11/2 cups for 4 servings), salt, and pepper. Bring to a boil, then cover and reduce to a low simmer. Cook until rice is tender, 15-18 minutes. Keep covered off heat until ready to serve.

While rice cooks, pat pork dry with paper towels; prick all over with a fork or knife. Season all over with salt and pepper. Heat a drizzle of oil in a large pan over medium-high heat. Add pork and cook until browned and cooked through, 4-6 minutes per side. Turn off heat; transfer to a plate. Wipe out pan.

Heat a drizzle of oil in same pan over medium-high heat. Add remaining ginger and cook until fragrant, 20-30 seconds. Stir in teriyaki sauce and simmer until slightly thickened, 1-2 minutes. Turn off heat.

Fluff rice with a fork; divide between plates along with carrots and pork. Top pork with sauce and sprinkle with scallion greens and remaining sesame seeds. Serve.