Heat a large skillet or wok over medium-high heat and add the toasted sesame oil.
Add the ground turkey to the skillet, breaking it into small crumbles with a spatula until it is fully browned and cooked through.
Stir in the minced garlic, grated fresh ginger, and the white parts of the sliced green onions, sautéing for about 1 minute until fragrant.
Add the chopped kimchi and gochujang to the pan, stirring constantly for 2 minutes to allow the kimchi to soften and the flavors to meld.
Incorporate the chilled jasmine rice and tamari, pressing the mixture firmly into the pan for 2-3 minutes to develop a light, crispy texture on the bottom.
In a separate small non-stick skillet, heat the avocado oil over medium heat and fry the egg and egg whites until the whites are opaque and the edges are golden.
Transfer the kimchi fried rice to a serving bowl, season with black pepper, and top with the fried egg and the remaining green onion greens.