Prepare the zucchini: Trim ends and cut zucchini the long way into 1/4-inch strips. Spread out strips on a large tray and brush lightly with olive oil and season well with salt and pepper.
On a grill or a grill pan, grill zucchini in a single layer until grill marks appear underneath, then flip over and repeat on the other side. Transfer zucchini to a platter and squeeze lemon juice over it.
Meanwhile, in a food processor or blender, combine basil and garlic with a few pinches of salt and black pepper until chopped. Drizzle in olive oil until it blends smoothly. Add 1 tablespoon vinegar and blend until well-mixed; taste and add more vinegar to taste. Season to taste.
Combine beans with about 2/3 of the dressing in a small bowl. In a larger bowl or serving platter, pour half of dressed beans in the bottom. Arrange grilled zucchini on top. Spoon remaining beans in the spaces. Drizzle the remaining dressing over the platter, to taste.
Finish with a light blanket of Parmesan and eat hot or at room temperature.