Preheat oven to 375°. In a medium bowl mix together bread crumbs and milk and set aside.
Meanwhile, lightly grease a large sheet pan with oil or nonstick spray and place broccoli, cauliflower, and carrots on sheet pan. Season with garlic powder, turmeric, ½ tsp salt and ¼ tsp pepper. Toss with 1 tbsp olive oil. Spread out on one half of the sheet pan.
To the breadcrumbs and milk, add ground beef, egg, oregano, half of the minced garlic, ½ tsp salt, ¼ tsp pepper, and mix until combined. Form into 6 meatballs and place on sheet pan. Bake for about 20 minutes or until meatballs are 160° internal temperature.
Meanwhile, heat 1 tbsp olive oil in a large saucepan over medium heat. Add remaining garlic cook briefly until fragrant. Add cremini mushrooms and cook for about 5-8 minutes or until mushrooms are softened and starting to brown.
Add tomatoes, rosemary or thyme, ½ tsp salt, and red pepper flakes. Simmer, stirring occasionally, until tomatoes are starting to become smooth.
When meatballs are done in the oven, add them to the tomato sauce and continue to simmer, as needed. Return vegetables to the oven for an additional 5-10 minutes or until lightly browned and tender.
Meanwhile, split hoagie rolls horizontally and hallow out some of the bread from the top bun. Place in the oven for about 5 minutes or until lightly toasted. Fill with meatballs and sauce, and top with provolone cheese. Return to oven for 2-3 minutes or until cheese is melted.
Serve meatball subs with roasted vegetables.