In a medium mixing bowl, combine the light mayo, whole grain mustard, honey, horseradish, hot sauce to taste, and ground cayenne pepper. Mix well until fully blended. Cover the sauce and place it in the refrigerator to chill while you prepare the rest of the meal.
In a large bowl, combine the ground turkey breast, grated onion, finely chopped jalapeño, barbecue sauce, Worcestershire sauce, liquid smoke, steak blend seasoning, and dry mesquite seasoning. Use your hands to gently mix until all ingredients are just incorporated. Form the mixture into 5 equally sized patties. I like to handle the mixture as little as possible for juicier burgers.
Heat olive oil in a skillet over medium heat. Add the sliced onion and cook, stirring frequently, until the onion becomes translucent, about 5 minutes. Reduce the heat to medium-low and continue cooking and stirring until the onion is very tender and a deep golden brown, about 15 to 20 minutes more. For extra depth of flavor, I sometimes deglaze the pan with a splash of water if the onions start to stick.
Heat a medium skillet over medium heat (use a little oil if your pan isn’t nonstick). Add the turkey patties from Step 2. Cook for about 6 minutes per side, or until the patties are browned on the outside and reach an internal temperature of 180°F (85°C). Turn the patties only once to keep them juicy.
Split the hamburger buns and place a cooked turkey patty from Step 4 on each bun base. Top each patty with a generous spoonful of the honey mustard sauce from Step 1 and a portion of the caramelized onions from Step 3. Cover with the top half of the bun and serve immediately. For even more flavor, I like to lightly toast the buns before assembling.