In a small saucepan, bring the wine, shallot, garlic, and brown sugar to a low rolling boil over medium to medium-high heat, stirring until the sugar is dissolved. Boil until the wine is reduced to about 1/2 cup, about 20 minutes. Remove from heat. Add the butter and whisk until smooth. Season the sauce with kosher salt and pepper.
In a medium bowl, season the beef; mix in half of the red wine sauce and the Worcestershire. Form into 4 patties (thinner in the centers for even cooking).
Layout sliced Eggplant on grill pan, brush both sides with olive Oil. Season with salt and pepper. Place grill pan on one side of grill on med heat. One eggplant starts to char, flip and cook other side. Eggplant is done with it softens and is charred on both sides.
On the other side of the pre-heated Grill, grill patties on one side, flip and baste with wine sauce. Turn the patties over and top with the remaining wine sauce, about 1 tbsp. each. Cook until desired doneness. Top each patty with 1 slice of cheese. Cover with foil and cook until the cheese melts, 2 to 3 minutes more.
Build the burgers with the bun bottoms, lettuce, patties, and grilled eggplant; season and set the bun tops in place.
Serve with any condiments you would like.
Paired with Slo Down Stand Out and Slo Down Chocolate Red Blend