Combine mayonnaise, mustard, honey, horseradish, Tabasco sauce and cayenne pepper in a bowl. Cover and refrigerate.
Mix turkey mince, grated onion, jalapeno, barbecue sauce, Worcestershire sauce, liquid smoke, steak seasoning and barbecue seasoning in a large bowl. Form into 5 patties.
Heat the olive oil in a frying pan over medium heat. Stir in the onion; cook and stir until the onion has softened and turned translucent, about 5 minutes. Reduce heat to medium-low then continue cooking and stirring until the onion is very tender and dark brown, 15 to 20 minutes more.
Cook the patties in a medium frying pan over medium heat, turning once, about 6 minutes per side. Serve on buns topped with spicy sweet aoili and caramelised onions.
Liquid smoke is a flavouring that has really taken off lately. Use it to add a smoky BBQ flavour to any meal.