Adjust an oven rack to the lowest position and the other oven rack to the upper. Place a parchment-lined baking sheet on the lowest rack. Line another baking sheet with paper-towels; set aside. Preheat the oven to 400°F.
Cut each eggplant in half and score the flesh of each eggplant half in a 1-inch diamond pattern and 1-inch deep. Brush the flesh side with 1 Tbsp olive oil and season with salt and pepper. Lay the eggplants, cut side down, on the preheated parchment-lined baking sheet. Roast until the flesh is tender, about 40 to 50 minutes. When the eggplants are finished roasting, lay them cut side down on the towel-lined baking sheet to drain.
While the eggplants are roasting prepare the bulgur. In a medium bowl or saucepan, toss the rinsed bulgur with 6 Tbsps boiling hot water; cover with a lid or plastic. Let the mixture sit for 30 to 40 minutes, until the grains are softened. Drain if necessary; set aside.
In a 10 to 12-inch skillet over medium heat, add 1 Tbsp olive oil; heat until shimmering. Add onion and cook until softened, about 5 minutes. Stir in the garlic, oregano, cinnamon, cayenne, and ½ tsp salt; cook until fragrant, about 1 minute. Remove from heat.
Add the onion mixture, chopped tomatoes, ¾ cup Pecorino Romano, pine nuts, vinegar, and bulgur to the skillet; let it heat through about 1 to 2 minutes. Taste for seasoning; add salt and pepper as needed.
Return the eggplants to the parchment lined baking sheet cut side up. Using a fork, gently push the eggplant flesh to the sides to make room for the bulgur stuffing. Scoop the bulgur with a large spoon to make mounds on each of the eggplants. Gently press the bulgar mixture to lightly pack.
Sprinkle the eggplants with the remaining ¼ cup Pecorino Romano cheese. Return to the oven for, 5 to 10 minutes on the upper rack. Sprinkle with chopped fresh parsley before serving. Recipe adapted from America's Test Kitchen.