Use a vegetable peeler to peel off strips of zucchini, trying to get the strips to be as wide and flat as possible, and including a bit of green on the edges of as many of the strips as possible. As you get into the middle of the zucchini the strips will just be the pale zucchini flesh. Stop before you get to the seeds. Place the zucchini strips into a serving bowl.
Add 1 tablespoon of the olive oil, lemon juice and vinegar (if using), basil, onion, and salt and pepper to the bowl and toss to combine. Add up to another tablespoon of olive oil if desired—it really depends on how dressed you like your salad. Taste and adjust seasonings as needed. Serve immediately, or let sit in the fridge or at room temperature for up to 2 hours.