In a large bowl, combine the pork, red pepper flakes, paprika, fennel, sage, onion, garlic and salt, to taste. Form the meat into 4 patties, put on a plate and coat with a drizzle of extra-virgin olive oil.
Heat a small pot over medium-low heat and add the brown sugar, Worcestershire, vinegar, tomato sauce and black pepper, to taste. Simmer until the mixture becomes a thick steak sauce consistency, about 15 minutes.
Add a couple inches of water to a medium skillet over medium-high heat. Bring to a boil, then salt the water and add the broccoli rabe. Cook for 5 minutes, then drain. Transfer the broccoli rabe to a cutting board and chop it into 2-inch pieces. Set aside. Return the skillet to the stove over medium heat and add 1 tablespoon of extra-virgin olive oil. Stir in the chopped garlic and the broccoli rabe. Saute for 2 minutes, then season with a few grates of nutmeg, to taste.
Heat a drizzle of extra-virgin olive oil in a skillet over medium-high heat, add the patties and cook for 5 to 6 minutes on each side. Top the patties with a slice of provolone during the last minute of cook time and tent with foil to melt.
Divide the broccoli rabe on the bottoms of the rolls and top with the cheesy sausage patties. Slather some of the warm sauce on the roll tops and cover the burgers. Serve the burgers on individual plates with a few chips alongside.