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Position rack in upper third of oven; preheat broiler to high. Line a baking sheet or broiler pan with foil and coat with cooking spray.
Mash garlic and 1/2 teaspoon salt on a cutting board with a fork to make a thick paste. Combine with 1 tablespoon oil, thyme and teaspoon pepper. Place the fish on the prepared pan and spread the paste on top of it.
Heat the remaining 1 tablespoon oil in a medium skillet over medium heat. Add shallot and cook, stirring, for 30 seconds. Add coconut milk, increase heat to medium-high and bring to a simmer. Reduce heat to medium-low and simmer until reduced to 3/4 cup, about 6 minutes. Season with the remaining 1/4 teaspoon salt and pepper to taste.
Meanwhile, broil the fish until just cooked through, 6 to 8 minutes. Spoon the sauce on top, sprinkle with coconut and serve with lime.