Bring a large pot of salted water to a rolling boil for the pasta. When boiling, add the pasta and cook until very al dente (about 2 minutes less than package directions); reserve about 1 cup of cooking water then drain the pasta and set aside.
While the pasta cooks, heat 1 tablespoon olive oil in a large skillet over medium heat. Add the chopped onion and a pinch of salt and sauté until translucent, about 4–5 minutes. Add the smashed garlic and cook 30 seconds more until fragrant.
Transfer the sautéed onion and garlic to a blender or food processor. Add the cauliflower, carrots, milk, heavy cream, and cream cheese. Blend until completely smooth (add 1/4 cup of the reserved pasta water if needed to help puree).
Return the skillet to medium-low heat, pour in the pureed vegetable mixture and gently simmer, stirring frequently, until the sauce thickens slightly — about 4–6 minutes. Stir in the grated Parmesan, nutmeg, lemon zest, and season with 1/2 teaspoon salt and black pepper. If sauce is too thick, loosen with up to 1/2 cup reserved pasta water.
In a separate small pan, quickly wilt the fresh spinach with the remaining 1 tablespoon of olive oil just until it collapses (about 1–2 minutes). Chop coarsely and fold into the sauce — this keeps the spinach texture while keeping the 'hidden' veggie approach.
Return drained pasta to the large pot (off the heat). Pour the hot veggie-cream sauce over the pasta and toss vigorously, adding 2 tablespoons reserved pasta water and the finishing olive oil/butter to create a silky emulsion that coats every piece. Taste and adjust salt and pepper.
Let the pasta rest for 2–3 minutes off the heat — the sauce will set slightly and cling to the pasta. Serve warm with extra Parmesan and chopped parsley scattered on top.