Heat oil in a large pot over medium heat. Add garlic, chopped carrot, cauliflower, and spinach, and cook for about 5 minutes, or until the garlic has lightly browned.
Add remaining ingredients, bring to a boil, then reduce heat to low, cover and cook for about 45 minutes, or until the largest piece of cauliflower can easily be pierced with a knife.
Remove from heat and pour into a blender, or use a stick blender, and blend/pulse until you reach your desired consistency (I made mine a bit chunky).
Serve over pasta and garnish with fresh parsley or basil, if you wish.