Preheat oven to 350 degrees. Toss garlic and Brussels Sprouts in olive oil, lemon juice, lemon zest, salt, pepper, red pepper flakes, and Italian seasoning. Spread out on a large baking sheet, so that it makes one layer. Roast for 25 minutes, or until Brussels Sprouts are fork-tender.
Remove baking sheet and add baby spinach, toss to combine. Return to the oven and roast 2-3 more minutes, or until spinach is slightly wilted.
Meanwhile, cook pasta according to instructions on the box. When the linguine and vegetables are done, toss them together with parmesan.