Whisk the eggs with the chicken broth well, mix in the pepper and sugar until the sugar is dissolved.
Cut the bananas at both ends and cut them into thirds lengthways in the skin. Place the banana pieces with the cut side down on a wet work board and carefully peel them.
Melt the butter in a pan, add 3 pieces of banana and fry for 2 minutes. Pour half of the egg mixture over it and let it set with the lid. Let the finished omelette slide onto a warm serving plate and drizzle with 2 tablespoons of date honey. Treat the 2nd serving in the same way.