In a bowl or shallow dish, whisk the coconut milk, lime juice, olive oil, a nice pinch of salt and a few grinds of pepper. Reserve 1 cup of the marinade. Add the fish to the bowl with the marinade and refrigerate for 20 minutes.
Remove the cod from the refrigerator. Place the cod in a 9 by 11-inch baking dish, discarding the marinade in the bowl. Place a slice of jalapeno over the top of each piece. Place in the oven and bake for 12 to 14 minutes.
Meanwhile, make the sauce. Pour the reserved 1 cup marinade in a small saucepan over medium heat and simmer until reduced and slightly thickened, about 5 minutes. Spoon some on the plate before placing the cod down on top. Serve warm.