In a shallow dish, combine 2 cloves of garlic, the ginger, 2 thinly sliced scallions, the soy sauce, 2 tablespoons sesame oil, the mirin, and brown sugar, and whisk to combine.

Add the chicken and toss to coat. Cover with plastic wrap and let marinate in the refrigerator for 30 minutes.

Bring a large pot of water to boil over high heat and season generously with salt. Prepare an ice bath in a large bowl. Blanch the spinach in the boiling water for 30 seconds, then transfer to the ice bath to shock, then drain. Transfer to a small bowl and season with 1 teaspoon of sesame oil, salt, and pepper.

In a medium skillet, heat 1 teaspoon of sesame oil over medium heat. Add the carrots and cook until softened, 2-3 minutes. Remove from the pan and set aside. Season with salt.

In the same skillet, heat 1 tablespoon of sesame oil over medium-high heat. Add the remaining clove of garlic and cook for 30 seconds, until fragrant. Add the mushrooms and cook, stirring frequently, until softened, about 2 minutes. Season with salt, then remove from the pan and set aside.

In the same skillet, heat the remaining tablespoon of sesame oil over medium-high heat. Add the marinated chicken and sauté, stirring occasionally, until cooked through, about 5 minutes.

Heat a nonstick pan over medium-high heat. Melt the butter in the pan. Once the foaming subsides, crack the eggs into the pan and cook until the whites are firm and golden brown around the edges and the yolks are still runny, or to your desired doneness.

To assemble the bibimbap bowls, top the rice with the chicken, kimchi, sliced scallions, carrots, spinach, mushrooms, cucumbers, and fried eggs.