Heat 1 tablespoon oil in a large skillet or wok over medium-high heat. Toss in the shrimp, season lightly with salt and pepper, and stir-fry for 2–3 minutes until they’re just pink and opaque. Remove from the pan and set aside.
In the same pan, add the remaining oil, whites of the green onions, and diced carrots. Sauté for about 3–4 minutes until the carrots begin to soften.
Stir in the garlic and ginger. Let them sizzle for about 30 seconds—it should smell amazing by now.
Push the veggies to one side of the pan and pour the beaten eggs into the other. Scramble until just cooked, then mix them into the veggies.
Add the chilled rice, breaking up any clumps as you go. Stir everything together and cook for 2–3 minutes to heat the rice through.
Return the shrimp to the pan along with tamari and sesame oil. Stir-fry for another minute until everything is well combined.
Top with the green parts of the onions, taste for seasoning, and serve hot!