Combine Mayonnaise, Mustard, Honey, Horseradish, Hot Pepper Sauce, And Cayenne Pepper In A Bowl. Cover And Refrigerate. Mix Ground Turkey, Grated Onion, Jalapeno, Barbeque Sauce, Worcestershire Sauce, Liquid Smoke, Steak Seasoning, And Mesquite Seasoning In A Large Bowl. Form Into 5 Patties. Heat The Olive Oil In A Skillet 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, And Continue Cooking And Stirring Until The Onion Is Very Tender And Dark Brown, 15 To 20 Minutes More. Cook The Patties In A Medium Skillet Over Medium Heat, Turning Once, To An Internal Temperature Of 180 Degrees F (85 Degrees C), About 6 Minutes Per Side. Serve On Buns Topped With Spicy Sweet Mayo And Caramelized Onions.