In a small saucepan, combine the smashed garlic cloves and the milk and simmer over low heat until the garlic is softened, about 20 minutes. Strain, reserving the milk. Using a food processor, puree the softened garlic; with the machine on, add the milk in a slow stream. Season with salt.
Preheat the oven to 400°. In a medium skillet, heat the sesame oil over medium heat. Add the chopped garlic, the scallions and ginger and cook, stirring, until fragrant, about 2 minutes. Stir in the mushrooms, cook for 3 minutes; add the soy sauce and cook for 2 minutes more.
Fill a deep, medium skillet with enough water to reach a depth of 2 inches, bring to a boil and season with salt. Add the bok choy and cook for 1 minute. Drain in a colander and run under cold water.
Butter an 8-inch square baking dish. Season the cod with salt and place in the baking dish. Bake until opaque and easily flaked with a fork, about 8 minutes. Transfer each fillet to a plate and top with the garlic puree. Serve with the bok choy, lime wedges and reserved mushrooms.