Whisk 1 cup warm water, egg, and 2 tablespoons oil in large bowl to blend

Add yeast, then flour, whisking until smooth

Cover and allow to stand at room temperature until batter has almost doubled in volume, approximately 2 hours

Stir in coconut, sesame seeds, and nutmeg

Cut bananas on deep diagonal into eighteen 1/2-inch-thick slices

Add banana slices to batter; stir gently to coat

Pour vegetable oil into heavy large saucepan to depth of 1 1/2 – 2 inches in depth

Attach deep-fry thermometer and heat oil to 350°F

Insert fork into 1 banana slice and transfer to oil

Repeat and cook up to 6 banana slices at a time, not overcrowding fritters

Fry until crisp and golden on all sides, about 3 minutes

Using slotted spoon, remove fritters to a plate lined with paper towels to drain

Repeat with remaining bananas in 2 more batches

Divide fritters among 6 plates

Serve warm with vanilla ice cream