Preheat oven to 425 degrees Fahrenheit and line a baking sheet with aluminum foil. Cut 2 of the sweet potatoes lengthwise so you end up with 4 halves. Rub in 2 tablespoons olive oil, ½ teaspoon salt, ¼ teaspoon pepper, 1 teaspoon garlic herb seasoning, ½ teaspoon italian seasoning, and ¼ teaspoon of cinnamon, thyme, rosemary, and oregano. Place facedown on the aluminum and bake for 25-30 minutes, or until fork-tender. Scoop out the insides and mash in a bowl with ½ cup of milk.
Preheat oven to 400 degrees Fahrenheit. Dice the other 2 sweet potatoes into small cubes (about ½") and rub with 2 tablespoons olive oil, ½ teaspoon salt, ¼ teaspoon pepper, 1 teaspoon garlic herb seasoning, ½ teaspoon italian seasoning, and ¼ teaspoon of cinnamon, thyme, rosemary, and oregano. Bake for 15-20 minutes, or until fork-tender.
In a large nonstick pan, heat 1 tablespoon olive oil on high heat. Add the onions and cook for 2-3 minutes, until they are translucent and browned. Add the mushrooms and 1 tablespoon oil. Cook for 2-3 minutes, until the mushrooms have shrunken and cooked down. Reduce the heat to medium high and add in the zucchini, spinach, arugula, and garlic. Cook for 2 minutes. Add the cooked diced sweet potatoes and ¼ teaspoon salt and pepper, 1 teaspoon garlic herb seasoning, ½ teaspoon italian seasoning, and ¼ teaspoon of cinnamon, thyme, rosemary, and oregano. Mix in the mashed sweet potatoes, parmesan, and remaining milk. For a thinner sauce, add some of the reserved pasta liquid, about ¼ cup or as needed.
Combine the cooked pasta with the sauce and season with the remaining seasonings and herbs, or to taste. Serve with grated parmesan.