In the base of a blender, blend the mustard, ketchup, honey, vinegar, butter, Worcestershire, hot sauce and garlic until liquefied. Divide the sauce between 2 bowls and set aside the second bowl.
Put the ground chicken into a large mixing bowl. Season with the salt and some pepper and mix until fully combined. Form patties using a 1/4-cup measure for each patty.
Heat the oil in a large saute pan. Add the patties to the pan and top each with a spoonful of the sauce. Cook, flipping the patties after 5 minutes. Top each with another spoonful of sauce and cook until the patties are cooked through, another 5 minutes. Transfer the patties to a platter and add the cheese slices if using. Repeat with any remaining patties.
Combine the reserved bowl of sauce with the mayonnaise and mix well.
Serve the patties on toasted slider buns with the "Barbie-Q" mayonnaise.