Heat 1 tablespoon of vegetable oil in a large wok or skillet over medium-high heat.
Add the ground lamb to the wok. Cook until fully browned, breaking it up into small crumbles as it cooks. Drain any excess fat if necessary.
Stir in the minced garlic and diced carrots. Cook for 3 to 4 minutes until the carrots begin to soften.
Push the meat and vegetables to one side of the wok. Add the remaining 1 tablespoon of vegetable oil, then add the chilled cooked white rice. Use a spatula to break up any clumps of rice.
Pour the soy sauce and oyster sauce over the rice. Toss everything together, stir-frying for 4 to 5 minutes until the rice is heated through and evenly coated.
Remove the wok from the heat. Drizzle with sesame oil and toss in the fresh basil leaves, stirring gently until the basil is just wilted. Serve immediately.