Bring a pot of heavily salted water to a boil.Chop zucchini into cubes, slice shallot and garlic cloves into thin slices. When the water is boiling, place the pasta in the pot to boil.
Heat olive oil in a large saute pan over medium heat and add the shallots and garlic to the pan. Suate until the garlic and shallot are soft and fragrant - about 3 minutes.
Add the cubed zucchini to the pan and saute until soft about 4 minutes. Add the spinach to the pan and saute until it is just soft and wilted. Add the salt to the pan and toss again.
Reserve 3/4 cup of the pasta water from the pot. Drain the pasta and set aside. Place warm sauteed veggies in a blender with the pasta water, basil, heavy cream and parmesan cheese.
Blend until a smooth and creamy sauce remains. Toss the warm noodles in the warm creamy sauce. Serve with extra parmesan cheese and lemon zest.
Notes
Blanch the basil for a brighter green color. Drop it in boiling water for 15-30 seconds and then transfer to ice water before blending. This keeps the sauce a vivid green instead of turning dull and olive-colored.
Save your pasta water. Before draining the pasta, scoop out a cup of the starchy cooking water. If the sauce gets too thick when tossing with the pasta, add a splash to loosen it up.
Do not let the cream boil. Once the cream is added to the pan keep it at a gentle simmer. A hard boil can cause the sauce to separate and lose its creamy texture.
Taste and adjust at the end. Add a little more salt, a squeeze of lemon, or an extra handful of parmesan before serving to get the flavor exactly right.