Combine all of the ground meat into a large mixing bowl. Shape into 16 (1-ounce) patties. Season patties generously with salt and pepper and drizzle with oil.
Cook burgers on a very hot grill for about 30 seconds on each side. If a smoky flavor is desired, you may place a lid on the grill during cooking. Serve the patties on Parker House rolls garnished with a dill pickle and Onion Relish.
Heat a large skillet over medium-high heat and add the olive oil and garlic cloves. Saute the garlic until lightly browned. Add the onions and continue to cook the mixture until golden brown. Season well with salt and pepper, add the water, stir, and bring to a boil, scraping up the caramelized bits on the bottom of the pan. Stir in ketchup and mustard. Simmer until thick. Remove from heat and let cool before serving with the burgers.