In a small pan, heat bbq sauce and bourbon. Bring sauce to a boil and boil 1 to 2 minutes so that all the alcohol cooks out; stirring constantly. Simmer sauce until meat and onions are ready.
Slice onion. Add 2 tablespoons butter to a large skillet. Add onions and saute on medium-low for 10 to 15 minutes or until onions are translucent, tender, and golden brown. When onions are golden brown, add jalapenos and heat until just warm. Set onions and peppers aside.
Heat grill to 400 degrees. (You can also cook on the stovetop. Heat skillet to medium-high.)
While the grill is heating, divide the meat into 6 equal patties, sized to fit your slider buns. (You can make regular size patties if desired.)
Salt and pepper both sides of meat. Cook burgers 3 to 4 minutes on each side.
Melt cheese over the burgers, then remove from heat.
Spread the remaining 2 tablespoons butter on buns and toast.
To make sandwich layer burger with cheese, onions and peppers, and bbq sauce on buns. Serve immediately.