Discard the outermost slices of zucchini; brush the rest with oil on both sides. Sprinkle the zucchini slices with salt and pepper. Grill until tender, about 4 minutes per side. You can prepare the zucchini a day ahead and store it in an airtight container in the refrigerator.
In a small bowl, combine the goat cheese, parsley, and lemon juice, mashing together with a fork.
Put 1/2 teaspoon of the cheese mixture about 1/2 inch from the end of a zucchini slice. Top with a few spinach leaves and a small (or half of a large) basil leaf. Roll up and place seam side down on a platter. Repeat with remaining zucchini slices. You can make these up to a day in advance; store in an airtight container in the refrigerator.
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