For the acorn squash relish:
6 tablespoons extra-virgin olive oil, divided
1 cup acorn squash cut into ⅛-inch cubes
Salt and freshly ground black pepper
1 tablespoon brown sugar
4 tablespoons deli mustard
1 tablespoon red wine vinegar
1 tablespoon minced parsley (optional)
For the burger:
1 ½ pounds ground pork
2 tablespoons cumin
1 pound fresh mozzarella
4 brioche hamburger buns
Lettuce, tomato, and thinly sliced red onion
Place 4 tablespoons extra-virgin olive oil in a non-stick pan over medium heat and add the acorn squash. Season with salt and pepper and cook until soft all the way through, about 1 to 2 minutes. Remove from heat and pour into a bowl. Add the brown sugar and toss to coat evenly. Add the deli mustard, red wine vinegar, parsley, and salt and pepper to taste. Mix well and set aside.
Place ground pork in a bowl, season with cumin, 1 tablespoon each salt and pepper, to taste. Mix by hand until spices are well incorporated. Form your ground pork into eight evenly-sized thin patties.
Cut the mozzarella into slices and put a quarter of the mozzarella into the center of four of the patties.
Place the remaining patties on top of the mozzarella and press down along the edges to form four mozzarella-stuffed pork burgers. Make sure to pinch the sides of each patty until the burger is completely closed off.
Brush outside of burgers lightly with olive oil and a pinch more salt. Put your burgers on a grill or griddle at high heat and let cook about 3 to 4 minutes on each side, or until they're just cooked though and their internal temperature reaches 145 degrees F.
While the burgers are cooking, cut the buns in half and drizzle each size with a little olive oil. Place the buns on the grill, cut side down and toast until lightly browned.
Place hot burger on a toasted hamburger bun and spoon acorn squash mustard on top.
Serve with lettuce, tomato and thinly sliced red onion.