Trim off the ends of the zucchini, then slice lengthwise into planks, leaving behind and discarding the seedy core.

Cut the zucchini planks into ½-inch cubes and set aside. In a medium bowl, toss the eggplant with ½ teaspoon each salt and teaspoon pepper.

In a large Dutch oven over medium-high, heat 6 tablespoons of the oil until shimmering. Add the eggplant in an even layer and cook, undisturbed, until golden brown, 3 to 5 minutes. Stir, cover and reduce to medium.

Cook, stirring, until tender when pierced with a fork but not falling apart, another 3 to 5 minutes. Using a slotted spoon, transfer to a paper towel–lined medium bowl and set aside.

To the same pot, add 1 tablespoon of the remaining oil and heat over medium-high until shimmering. Add the zucchini in an even layer and cook undisturbed until well-browned, about 4 minutes.

Stir and cook, stirring, until browned on all sides and tender when pierced with a fork, another 1 to 2 minutes. Using the slotted spoon, transfer to the bowl with the eggplant.

To the same pot, add the remaining 1 tablespoon oil and heat over medium-high until shimmering. Add the onion and ¼ teaspoon salt. Cook, stirring occasionally, until golden brown, 3 to 5 minutes. Stir in the bell peppers, ½ teaspoon each salt and teaspoon pepper.

Cover and cook, stirring, until the peppers soften, 3 to 5 minutes. Stir in the garlic, cumin and oregano, then cook until fragrant, about 30 seconds. Stir in the tomatoes with their juice, then cover and simmer over medium until the flavors have melded, 5 to 7 minutes.

Reduce to low and stir in the eggplant-zucchini mixture. Cook until heated through, 1 to 2 minutes. Stir in the parsley, then taste and season with salt and pepper. Transfer to a platter and top with the Manchego.