1. Heat 3 Tbsp. olive oil in a stockpot or Dutch oven over high heat and add the ground venison. Brown the venison very well, stirring occasionally, about 15 minutes. Lower the heat to medium, season with salt and pepper, and add the onions, garlic, oregano, and tomato paste. Cook until the onions are tender, stirring occasionally, about 10 minutes. Add the crushed tomatoes and parsley and cook, stirring often, for 10 minutes more. Set aside to cool slightly. Adjust the seasoning.
2. Meanwhile, preheat the oven to 400 degrees. Toss the eggplant in the remaining olive oil and season with salt and pepper. Lay the slices out in a single layer on a baking sheet and roast until tender, about 30 minutes. Set aside to cool.
3. Make the béchamel: Melt the butter in a pot over medium-low heat, then add the flour, whisking constantly. Cook this roux for a couple of minutes, then add about 1 cup of the milk, whisking the sauce smooth until it thickens. Add 2 more cups of milk; continue to whisk, allowing the béchamel to thicken. Add the remaining milk, and cook at a gentle bubble until it is quite thick, 10 to 15 minutes. Season with salt and pepper and set aside to cool. Whisk the sauce occasionally to keep it smooth.
4. Reduce the oven to 350 degrees. Put the venison mixture in the bottom of a high-sided 9x12-inch baking pan. Layer the eggplant over the venison. Add the egg yolks to the béchamel and whisk again to combine. Pour the béchamel over the eggplant. Sprinkle the cinnamon, nutmeg, and Parmesan on top and bake for about 45 minutes. Serves 8