Make the sauce: In a medium saucepan over medium heat, melt the butter. Add the onion and garlic and saute until softened, about 3 minutes. Add the rest of the sauce ingredients; bring to a boil, then simmer until the sauce is reduced to 2 cups, about 30 minutes.
Meanwhile, preheat a grill to medium-high. Season the steaks with salt and pepper and rub with the oil. Grill for 3 to 5 minutes per side for medium-rare. Let rest for 10 minutes before slicing. Serve with the beer-molasses sauce and the grilled eggs.
Place a cast-iron skillet on the grill; add butter, oil or bacon drippings. Crack in eggs and season to taste (the Neelys use a blend of paprika, sugar and onion powder, plus salt and pepper). Cook until the edges are crisp but the yolks are still runny, 2-3 minutes.