Preheat oven to 425 degrees F. Coat a large rimmed baking sheet with cooking spray.

Cut zucchini in half lengthwise and remove seeds. Cut crosswise into 1-inch slices.

Combine 1 tablespoon oil, 1 1/2 tablespoons mustard, garlic, rosemary, lemon zest, 1/2 tablespoon lemon juice, 1/2 teaspoon pepper, and 1/4 teaspoon salt in a large bowl. Add chicken and the zucchini and stir to coat. Arrange in a single layer on the prepared pan.

Bake, without stirring or flipping, until the zucchini starts to brown and the chicken reaches an internal temperature of 165 degrees F, 20 to 22 minutes. Transfer the chicken to a clean cutting board and slice.

Meanwhile, whisk the remaining 2 tablespoons oil, 1/2 tablespoon mustard, 1 1/2 tablespoons lemon juice, maple syrup, thyme, and the remaining 1/2 teaspoon pepper and 1/4 teaspoon salt in a medium bowl. Add greens and toss to coat.

Divide the greens among 4 serving plates. Top with the chicken and zucchini, Parmesan, and pumpkin seeds.