For the Southern slaw: Add the cabbage, jalapeno, mayonnaise, white vinegar and sugar to a large bowl and toss to combine. Season with salt and pepper. Set aside until ready to serve.
For the burger: Place a large saute pan over medium heat. Once the pan is hot, add the olive oil followed by the onions and saute until just starting to brown, about 3 minutes. Add the agave and balsamic vinegar and toss to combine. Cook for about 10 minutes or until they reach your desired caramelized color. Set aside until ready to serve.
Divide the beef into 8 even sections and form into patties. Sprinkle the patties on both sides with salt and pepper. Heat a large nonstick skillet over medium-high heat and add 2 ounces canola oil. Let get hot, then add the patties and cook 5 minutes per side or until they reach your desired doneness, frying in batches and adding oil as needed. Remove the patties from the skillet and top each with a slice of American cheese.
Fry the eggs over-easy in the same skillet over medium-high heat, about 4 minutes.
Place some mayonnaise on the bun bottoms and tops. Add 2 cheese-topped patties, a fried egg, onions and slaw to each, and finish with the bun tops. Serve.