For the rice: Bring 3 cups of water to a boil in a large pot. Using a fine-mesh sieve, rinse the rice under cold water until the water runs clear. Stir the rice in the boiling water and reduce the heat to a simmer. Cover and cook until the liquid is absorbed, about 12 minutes. Fluff with a fork and cover with a lid to hold warm for plating.
For the stir-fried vegetables: Heat a wok until smoking. Remove the wok from the heat and add the grapeseed oil. Place the wok back over the heat, add the garlic and ginger and cook for 30 seconds, stirring to avoid burning the garlic. Add the carrots, mushrooms, onions and bok choy and stir-fry until the carrots are tender, 3 to 5 minutes. Season with salt and pepper and transfer to a bowl; cover to keep warm.
For the sauce: Heat the wiped-clean wok over high heat. Add the chicken broth, sherry, fish sauce and ginger and bring to a boil. In a small bowl, mix the cornstarch with 1/2 cup water and add it to the sauce slowly, whisking, until the sauce reaches the desired thickness (do not add it all if it thickens up enough first). Whisk the egg yolks into the sauce, then remove from the heat and season with salt, pepper and lime juice.
For the fish: In a tall-sided pot, heat the vegetable oil over medium heat until a deep-fry thermometer inserted in the oil registers 350 degrees F; line a plate with paper towels. In a shallow dish, season the cornstarch with the salt and pepper. Dredge the cod fillets in the cornstarch and immediately place them in the oil, making sure not to overcrowd the pot. Cook the fish until it floats and cooks to a golden brown. Transfer the fish to the paper towels and sprinkle with additional salt and pepper.
Scoop about 3/4 cup of rice onto the center of each of 6 plates. Top the rice with the stir-fried vegetables. Place the fried fish on top of the vegetables and spoon about 3 ounces of the sauce around the fish. Garnish the plate with the chopped scallions.