Heat 1 tablespoon of the coconut oil in a large nonstick skillet or wok over medium-high heat. Add the eggs and cook, stirring and folding often to form small curds, until set, about 1 minute. Transfer eggs to a plate and set aside.
Melt the remaining 1 tablespoon of coconut oil in the same skillet. Add the onion and carrot and cook, stirring occasionally, until starting to soften, about 4 minutes.
Add the garlic and curry paste and sauté until the curry paste has coated all of the vegetables, about 1 minute. Add mirin and cook until evaporated, about 1 minute.
Add the rice and salt and cook, stirring constantly, until the rice is nicely coated in oil and crispy in spots, 2 to 3 minutes. Add the chicken, peas, and reserved scrambled egg and stir until heated through, 1 to 2 minutes.
Transfer to a serving platter or plates and garnish with the basil. Serve immediately.
