Fresh Coconut Layer Cake

Preheat oven to 350 °F with racks in upper and lower thirds. Pierce softest eye of each coconut with a small screwdriver and collect liquid in 2 separate bowls to sample. If either tastes rancid, discard that coconut and liquid and Start over with another. Strain liquid from 2 coconuts through a dampened-paper-towel-lined sieve into a 1-cup measure and set coconuts aside. (You should have about 3/4 cup liquid. If not, add water.) Bring to a simmer with sugar and a pinch of salt in a small saucepan, stirring until sugar has dissolved. Cool and reserve. Bake coconuts on lower rack 15 minutes. Leave oven on. Break shells with a hammer, then remove flesh with screwdriver, prying it out carefully. Peel brown membrane from flesh with a vegetable peeler. Coarsely grate enough coconut on large holes of a box grater to measure 5 cups.