Adjust rack to top position and preheat oven to 425 degrees. Wash and dry produce. • Trim, peel, and cut carrots on a diagonal into ½-inch-thick pieces. Peel and mince garlic. Peel and mince ginger until you have 1 TBSP (2 TBSP for 4 servings). Trim and thinly slice scallions, separating whites from greens. Zest and quarter lime.
Toss carrots on a baking sheet with a drizzle of oil, salt, and pepper. Roast on top rack until browned and tender, 20-25 minutes. • Meanwhile, melt 1 TBSP butter in a small pot over medium-high heat. Add garlic and half the minced ginger; cook, stirring, until fragrant, 30 seconds. • Add rice, ¾ cup water (1½ cups for 4 servings), and a big pinch of salt. 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 chicken* dry with paper towels and season all over with salt and pepper. • Heat a drizzle of oil in a large, preferably nonstick, pan over medium-high heat. Add chicken and cook until browned and cooked through, 3-5 minutes per side. • Turn off heat; remove from pan and set aside. Wipe out pan.
Heat a drizzle of oil in same pan over medium heat. Add scallion whites and remaining minced ginger; cook, stirring, until fragrant and softened, 1 minute.
Add stock concentrate, half the jam (all for 4 servings), ¼ cup water (1⁄3 cup for 4), and a squeeze of lime juice to pan with aromatics. Cook, stirring, until combined and thickened, 3-4 minutes. • Remove from heat; stir in 1 TBSP butter (2 TBSP for 4) until melted. Taste and add more lime juice if desired.
Fluff rice with a fork and season with salt. • Toss carrots with lime zest. • Divide rice, carrots, and chicken between plates. Drizzle chicken with sauce and sprinkle everything with scallion greens. Serve with any remaining lime wedges on the side.