Place a rimmed baking sheet on the middle rack and heat the oven to 450°F. Brush the cut sides of the eggplant with oil and season with salt and pepper. Place the eggplant cut-side down on the preheated baking sheet and roast until the flesh is tender and the skins are slightly shriveled, about 15 to 20 minutes.

Transfer the eggplant to a paper-towel-lined plate, cut-side down, and let drain for 5 minutes. Flip them over and scoop out the flesh with a spoon, leaving a 1/2-inch-thick shell. Chop the scooped flesh into bite-sized pieces.

Combine the bulgur and water in a small bowl. Cover and let stand until the water is completely absorbed and the grains are tender, about 15 to 20 minutes.

Heat the remaining oil in a large skillet over medium heat until it shimmers. Add the onion and a pinch of salt, cooking until softened and translucent, about 5 minutes. Stir in the garlic, oregano, cinnamon, and cayenne and cook until fragrant.

Remove the skillet from the heat and fold in the chopped eggplant flesh, soaked bulgur, tomatoes, half of the Pecorino cheese, pine nuts, vinegar, and parsley. Season the filling with salt and pepper to taste.

Reduce the oven temperature to 400°F. Arrange the eggplant shells cut-side up on the baking sheet and mound the filling into the cavities. Sprinkle with the remaining cheese and bake until the cheese is browned and the filling is hot throughout, about 10 to 15 minutes. Serve warm.