Fill a large pot with water, add salt, and bring to a boil.
Chop all vegetables into similar-sized pieces; mince garlic.
Add spaghetti to boiling water and cook per package, minus 1 minute.
Heat olive oil in skillet, add broccoli first; cook 3 minutes.
Add bell peppers and mushrooms; cook 4 more minutes.
Push veggies aside, sauté garlic for 30 seconds.
Stir in crushed tomatoes, herbs, and cherry tomatoes.
Add zucchini slices and simmer over medium heat.
Drain pasta, reserving 1 cup water; add pasta to sauce.
Toss with spinach until wilted; adjust seasoning; serve with parmesan.