Preheat the oven to 425 degrees F.
Toss the eggplant with the olive oil and season with salt and pepper and place onto a baking sheet. Place the baking sheet into the oven and roast for 10 minutes.
Remove the baking sheet from the oven and toss with the garlic and oregano and place back into the oven for another 10 minutes, until the eggplant is lightly golden brown and soft. Remove from the oven, add the parsley and gently toss to combine. Let cool slightly.
Place the eggplant into a bowl and toss with the cheeses. Set aside.
Combine the ingredients in a blender and blend until smooth. Set aside.
Bring the vinegar to a boil in a small nonreactive saucepan and cook until thickened and reduced to about 3/4 cup. Stir in the honey and set aside.
Whisk all ingredients together in a large bowl. Set aside.
Divide the eggplant filling among the peppers, compressing it into the shape of the pepper (the roasted pepper is very delicate and may begin to tear, but it will be fine).
Place the flour onto a plate and season with salt and pepper. Dredge the pepper completely in the flour and tap off any excess. Dip the peppers into the beer batter and allow excess to drain off. Place the cornmeal on a plate and season with salt and pepper and dredge the pepper in the cornmeal.
In a large frying pan, heat the oil to 370 degrees F.
Fry the peppers in batches, turning until lightly brown, about 4 minutes. Drain on paper towels. Spoon some of the sauce in the middle of the plate. Place a relleno on top of the sauce and drizzle the relleno with some of the balsamic reduction. Garnish with parsley.