Bring a large pot of water to a boil. Season with 1/2 teaspoon salt.
Slice the tops off the bell peppers and reserve, discarding the stems. Remove the seeds and ribs and discard. Blanch the bell pepper bottoms in the boiling water, working in batches if necessary, until crisp-tender, about 3 minutes. Remove the peppers from the water and set aside to cool.
Chop the reserved pepper tops; you should have about 1 1/3 cups. Heat the oil in a medium pot over medium-high heat. Add the chopped pepper tops, onions, and celery and cook until the vegetables are soft, about 5 minutes. Add the garlic and cook for 1 minute. Add the ground beef and cook, stirring, until the beef is browned and all the pink has disappeared, about 5 minutes. Add the eggplant and season with the remaining 1 tablespoon salt, Essence, and cayenne. Cook, stirring occasionally, until the eggplant is very soft, about 30 minutes. The filling should be moist-if it begins to dry out and stick to the bottom of the pan, add a bit of water. Remove the eggplant mixture from the heat and add 1 cup of the bread crumbs-this should be just enough to bind the mixture lightly. Cool the mixture for about 10 minutes.
Fill the bell pepper bottoms with the eggplant stuffing and place in a large casserole or baking dish. Combine the remaining 2 tablespoons bread crumbs with the Parmesan and divide this mixture evenly among the tops of the peppers. Add enough water to just cover the bottom of the casserole and bake the peppers, uncovered, for about 30 minutes, or until heated through and the tops are lightly golden.
Makes 10 large stuffed peppers, 10 servings