Heat a large skillet over medium-high heat. Drizzle in EVOO. Cook the bacon until almost crispy. Transfer to a plate and let cool.
Stir the onions into the bacon drippings and season with pepper. Reduce the heat to medium-low and cook until caramel in color, about 30 minutes. Season the onions with salt and deglaze the pan with a little wine. Transfer to a bowl and cover to keep warm.
Meanwhile, combine the beef, cooled bacon, rosemary, salt and pepper. Score the mixture into four equal portions and form them into patties slightly thinner at the center than at the edges for even cooking and to ensure a flat surface (burgers plump as they cook). Coat the burgers with EVOO.
Return the skillet to the burner and increase the heat to medium-high. Add the burgers and cook, flipping once, for 8 minutes for medium-rare (adjust the timing for more well-done burgers).
Place the burgers on the toasted rolls and top with the caramelized onions, some gorgonzola crumbles and spicy greens.