1. Preheat grill pan over medium-high heat. Combine first 4 ingredients in a bowl; toss well to coat. Arrange zucchini in a single layer in pan; grill 4 minutes, turning after 2 minutes.
2. Chop ciabatta bread. Place bread and thyme in a food processor; pulse 10 times. Heat a skillet over medium-high heat. Add olive oil. Add bread mixture; cook 5 minutes, stirring frequently. Combine zucchini, bread mixture, and Parmigiano-Reggiano.