Preheat the oven to 400 degrees. Slice the eggplant thin, lengthwise. If you have a mandolin, that will work great for this. If not, than just slice it as think as you can.
Lightly oil a baking sheet. Season the eggplant with kosher salt and freshly cracked black pepper. Lay on the sheet pan and season the other side. Drizzle with olive oil on the top and do a quick roast of the eggplant. It will only take about 8-10 minutes. You are just looking to start cooking it. It will help make it pliable to roll as well as give you a little roast on it.
When you pull the eggplant out of the oven, knock the temp down to 375 degrees.
Meanwhile, while the eggplant roasts, make the filling. Brown the ground beef, season with kosher salt and freshly cracked black pepper and drain off any excess grease. Lower the heat to low and add in the tomato puree and cook for about 4-5 minutes or until the tomato bite cooks out of the beef. Season with salt and pepper if needed. Remove from the heat and let cool for about 5-10 minutes.
Add in the breadcrumbs and the Parmesan cheese. Check the seasoning and let it cool until it is about room temp. About another 5-10 minutes. This can be while the eggplant cools to where you can handle it.
In a baking dish or pie pan,(i usually use a pie pan or tin for this, it works great. You can also use a baking dish). Ladle about 1/4-1/2 cup of the homemade marinara into the bottom of the pan. Spread it our evenly. Start rolling the eggplant and laying them into the pan.
Take the eggplant and lay 2 heaping teaspoons or more if your slices are bigger of the filling into the top 1/3 of the piece of eggplant. Take the top of the eggplant slice and pull it over the filling. Pull it tight, but don't rip it and roll over the filling. You want them to be really filled without it coming out of the ends.
Lay the rolls into the baking pan either in a row if you are using a baking pan or in a circle if using a pie pan. Once you have all of your rolls done, spoon the rest of the marinara sauce over the rolls, I like to keep the ends of the rolls slightly exposed without sauce.
Top with the mozzarella cheese and then top that with the Asiago. Cover with plastic and foil. Bake for 30-35 minutes and then uncover and bake for about 10-15 minutes until the cheese is bubbly. Served immediately with pasta or a side salad. ENJOY!!!