Preheat oven to 375 degrees.
Heat a large cast-iron skillet to a medium heat. Add 2 teaspoon oil, let heat for 30 seconds. Add onion, carrot, celery and ½ teaspoon salt. Sauté until slightly softened, about 3 minutes, add garlic and cook another minute. Set aside and let cool slightly.
In a medium bowl, add turkey, egg, parmesan cheese, cracker crumbs, 1 teaspoon Italian seasoning, 1 teaspoon salt, veggie mixture. Pour milk over cracker crumbs. Use your hands to combine the mixture, do not over mix. Use a ¼ cup measure to form mixture into meatballs.
Heat remaining oil in the same cast-iron skillet over a medium-high heat. Sear meatballs until brown and crisp on all sides. If needed, work in batches. Once all the meatballs are brown, remove from pan and cover with foil. Reduce heat to a medium-low and add onion and garlic. Saute for 2 minutes until softened. Add wine. Reduce for 30 seconds.
Add remaining salt, Italian seasoning, tomato paste, water and sugar to the pan. Bring to a boil and reduce to a simmer. Add all the meatballs back to the pan, along with any accumulated juices. Simmer until meatballs are cooked through, another 7-10 minutes.
Whilte the meatballs simmer, use a serrated knife, cut a V in the center of each hoagie so you have a place to nestle meat balls. If you're using a regular sub roll, you don't have to do this. Brush the inside of the hoagies with butter. Sprinkle with salt and pepper. Pop in the oven and bake until crisp, about 10 minutes.
Once meatballs are cooked though, fill the hoagies with 3 meatballs. Top with cheese and put on a large baking sheet. Repeat with remaining meatballs and buns. Bake until cheese is melted, about 10 minutes. Garnish with more grated parmesan cheese.