Heat 1 tablespoon of vegetable oil in a large wok or skillet over medium-high heat.
Add the minced garlic and diced carrots, stir-frying for 2 to 3 minutes until the carrots begin to soften.
Stir in the green peas and the cold, cooked rice, using a spatula to break apart any clumps.
Pour the soy sauce and sesame oil evenly over the rice, tossing continuously for 2 minutes until all ingredients are well combined and the rice takes on a uniform color.
Drizzle the remaining 1 tablespoon of vegetable oil around the edges of the wok. Press the rice mixture firmly into a flat, even layer against the bottom of the pan.
Let the rice cook completely undisturbed for 3 to 4 minutes to form a crispy, golden-brown crust on the bottom.
Gently scrape the bottom of the pan to mix the crispy bits into the rest of the rice. Remove from heat, garnish with chopped green onions, and serve hot.