Trim off stem end of fennel; quarter fennel but do not remove core. Place fennel in a small microwave-safe dish or pie plate. Add the water. Cover with vented plastic wrap. Microwave on 100 percent power (high) about 4 minutes or until nearly tender; drain.
Meanwhile, for dressing, in small bowl combine oil, lemon peel, lemon juice, 1/4 teaspoon salt, and 1/8 teaspoon pepper; whisk until smooth. Brush fennel and asparagus with 1 tablespoon of the dressing; set remaining dressing aside.
Grill fennel on the rack of an uncovered grill directly over medium heat for 5 minutes, turning occasionally. Add asparagus to the grill; grill vegetables for 7 to 8 minutes more or until vegetables are tender, turning occasionally.
Transfer fennel to a cutting board; cool slightly and slice into 1/4- to 1/2-inch-thick slices, discarding core. Divide fennel and asparagus among 4 dinner plates. Arrange spinach on top. Drizzle with remaining dressing. Top with Parmesan cheese and basil. Makes 4 servings.