Preheat oven to
350F. In a large bowl, beat the eggs with an electric mixer until light
colored. Gradually beat in the sugar and the coconut milk a little at a
time. Whisk in the vanilla. Slice bananas about 1/2 inch thick and fold
into batter. Pour pudding into a deep, well-buttered souffle dish, and
place dish in a pan with enough hot water to come 2 inches up the side of
the souffle dish. Bake for 45-50 minutes, or until a tester comes out
clean. Cool and refrigerate until serving.