Place one oven rack in middle position and a second rack below. Preheat oven to 200°C (400°F) and line two baking sheets with parchment paper.

Break cauliflower into large florets and cut each into 1-cm (1/2-in.) thick slices.

Cut each zucchini into eight long matchsticks and then cut in half widthwise to end up with 16 quarters per zucchini.

Add a drizzle of oil to vegetables and combine until coated.

In a large bowl, combine spices, salt, breadcrumbs, and Parmigiano Reggiano. Add cauliflower slices and combine to coat with your hands. Repeat with remaining vegetables.

Place cauliflower on one sheet and Brussels sprouts on the other, and season with pepper. Place the sheet with cauliflower on the bottom rack, and the one with Brussels sprouts on the middle rack. Bake for 20 minutes.

Remove vegetables from the oven to turn. Add zucchini quarters to sheet with Brussels sprouts, and return to oven, switching the order of the sheets, i.e., Brussels sprouts on the lower rack and cauliflower on the middle rack. Bake for another 15 minutes or until vegetables are tender and nicely roasted.