In the bottom of a large bowl, whisk together the mayonnaise (1 tablespoon), lemon juice (2 tablespoons), kosher salt (1/2 teaspoon), and black pepper (1/4 teaspoon). Gradually add the olive oil (2 tablespoons), whisking as you add it so it's emulsified.
Cut the zucchini into "ribbons." It's easiest to use a vegetable peeler for this, but you can also use a sharp knife or a mandoline (see notes about seeds).
Add the zucchini ribbons to the dressing and toss well to coat.
Transfer the zucchini ribbons to a platter and sprinkle with shaved parmesan cheese (I used a vegetable peeler for this task, too) and toasted pine nuts (see notes).
You can substitute the mayonnaise for 2 tablespoons Greek yogurt, if you prefer. You can also make it vegan by using 1 teaspoon dijon mustard instead, or a vegan-friendly mayo (and omitting the parmesan cheese).
Money saving tip: Pine nuts can be a bit pricy- you can easily use slivered almonds, or even walnuts or pecans, instead.
About the zucchini seeds: You can cut these into ribbons and use them in the salad. But if the zucchini is big, the seeds may not be a suitable texture to cut into ribbons. Or, it may just be too difficult to cut the seeded part into ribbons. If this is the case, and the seeds aren't TOO big, you can save the seeds and pulp for use in another use. I personally like to chop them up and add them to scrambled eggs.
How to toast pine nuts: You may be able to find pine nuts already toasted in the store. But if you can't, just add the pine nuts to a dry skillet and toast on medium heat, shaking the pan or stirring them around frequently, until they are golden brown. Keep an eye on them, because they can burn easily!
Traditional parmesan cheese may not be suitable for a strict vegetarian diet because it contains animal rennet. Look for a suitable vegetarian substitute, such as a parmesan made with plant rennet.
The provided nutrition information does not include any added sodium from seasoning to taste, any optional ingredients, and it does not take brands into account. Feel free to calculate it yourself using this calculator or by adding the recipe to Yummly.