Bring a large pot of salted water to a boil. Drop in the spinach, basil, and garlic cloves, and let them cook for just 30 seconds until the spinach turns bright and wilted. Immediately scoop them out with a slotted spoon and transfer them into a blender. This quick blanch locks in that vivid green color instead of letting it turn dull and brownish.
Using the same pot of boiling water, cook your pasta according to the package directions until al dente. I like to keep a little bite in mine since it will continue to soften slightly once mixed with the warm cheese sauce. Drain the pasta and set it aside while you finish the sauce.
Add the lemon juice and a splash of the reserved pasta water to the blender with your blanched spinach, basil, and garlic. Blend until you get a completely smooth, vibrant green purée with no chunks left. Set this aside; it is the secret to the neon color without using any food coloring.
In a medium saucepan over medium heat, melt the butter until it foams slightly. Whisk in the flour and cook for about a minute, stirring constantly, until the mixture smells lightly toasted and turns a pale golden color. This step cooks off the raw flour taste and sets up the base for a smooth sauce.
Slowly pour in the warmed milk while whisking constantly to prevent lumps. Keep whisking over medium heat until the mixture thickens enough to coat the back of a spoon, which usually takes 3 to 4 minutes. Lower the heat and stir in the mozzarella, cheddar, and parmesan a handful at a time, letting each addition melt before adding more.
Pour the blended spinach-basil purée into the cheese sauce and stir well until the color is fully incorporated and glowing green. Season with salt, pepper, and a pinch of nutmeg if using, then give it one final taste to adjust the seasoning.
Add the drained pasta directly into the saucepan with the green cheese sauce. Toss everything together gently until every piece of pasta is coated in that bright, creamy sauce. Serve immediately while it is warm and glossy.