Cook rice & carrots: Bring a medium saucepan of salted water to a boil. Scrub carrot, quarter lengthwise, and cut crosswise into ¼-inch pieces. Add rice to boiling water, and cook (like pasta), stirring occasionally, until almost tender, about 8 minutes. Add carrots and cook rice and carrots together until tender, about 4 minutes more. Drain, rinse with cold water, and drain again.

Prep ingredients: While rice cooks, trim scallions, then thinly slice, keeping dark greens separate. Trim snow peas, then halve crosswise. Peel and finely chop 2 teaspoons garlic. Peel and finely chop 1 tablespoon ginger. Beat 2 large eggs in a small bowl. Pat shrimp dry and season lightly with salt and pepper.

Make sauce: In a small bowl, stir to combine all of the tamari, sesame oil, 1 tablespoon vinegar, 1 tablespoon water, and 2 teaspoons sugar.

Cook eggs & shrimp: Heat 2 teaspoons neutral oil in a large nonstick skillet over medium-high. Add eggs and scramble until soft curds form, about 1 minute. Transfer to a plate and break into large pieces. Wipe out skillet. Add shrimp and 1 tablespoon oil to same skillet, and cook over high heat, stirring, until shrimp are firm and just cooked through, 2–3 minutes. Transfer shrimp to plate with eggs.

Cook vegetables: Add snow peas, ginger, garlic, and scallion whites and light greens to same skillet. Cook, stirring, until snow peas are bright green, 1–2 minutes. Transfer to plate with shrimp. Add rice, carrots, sauce, and 1 tablespoon neutral oil; cook over high heat, pressing down to allow rice to crisp, tossing occasionally and repeating, until the rice is warmed through, about 5 minutes.

Finish & serve: Stir shrimp, snow peas, and eggs into rice, and toss until warmed through. Season to taste with salt and pepper. Serve fried rice topped with scallion dark greens.