In a small bowl, whisk together the tamari, gochujang, and toasted sesame oil until the paste is fully incorporated.
Heat a large non-stick skillet over medium-high heat with half of the avocado oil and sauté the shrimp for 2-3 minutes until pink and opaque, then remove from the pan.
Add the remaining avocado oil to the same pan and fry the eggs until the whites are set and the edges are golden, then carefully set them aside.
Add the minced garlic, grated ginger, and the white parts of the sliced scallions to the pan, stirring for 30 seconds until fragrant.
Stir in the chopped kimchi and the chilled brown rice, pressing the rice down with a spatula to ensure it makes contact with the pan to crisp for 2-3 minutes.
Return the cooked shrimp to the pan and pour the tamari mixture over the rice, tossing everything together until the sauce is evenly distributed and the dish is steaming.
Divide the rice into bowls and top each serving with a fried egg and the remaining green scallion tops.