Warm tortilla. Roll banana with chocolate chips, place in tortilla. Fold ends over, seal with egg yolk. Deep fry until golden brown and chocolate is melted, about 4 minutes at 350 degrees F.
Cut in center on a bias. Place burrito with points up on a dessert plate, pooled with caramel sauce. Add scoop of vanilla ice cream next to burrito. Sprinkle with pecans, decorate with chocolate syrup.
