In a large skillet heat the butter over medium high heat. Add the shallot and garlic and saute for 1 minute until fragrant. Add the rice to the skillet, and stir for 1 minute to just toast the rice.
Once the rice has slightly toasted, add the white wine and stir to combine. Wait until all the wine has been absorbed and then start adding the chicken stock 1/2 cup at a time, making sure to let each batch of chicken stock absorb before adding the next. Continue to stir the risotto the entire time, about 25-30 minutes. Once you've added all your stock, and the rice is tender, remove from the heat and stir in the Parmesan and mascarpone cheese. Season with salt and pepper as needed and transfer to a bowl to cool.
Slice the ends off of the eggplant. Slice the eggplant into 1/4-inch lengthwise slices (long slices, not circles), about 6 slices total per eggplant. Liberally salt the slices and transfer them into a colander for about 1 hour. Rinse the salt off the eggplant and press with paper towels to dry.
Heat a skillet on the stove with high heat. Brush both sides of the eggplant liberally with olive oil and sprinkle with salt and pepper. Cook for 2-3 minutes on both sides until the eggplant is pliable. Remove the eggplant once cooked and place on a large baking sheet to cool.
Preheat oven to 350 degrees F.
Place half of the marinara sauce on the bottom of a small baking dish. Add a few spoonfuls of the cooled risotto on top of the eggplant slices, roll the eggplant up and place seam side down in baking dish. Repeat this with the remaining risotto and eggplant and then add a spoonful of the remaining marinara sauce on top of each. Dust with shredded Parmesan cheese. Transfer the baking dish into the oven and bake for 25 minutes. Serve with additional Parmesan cheese and shredded basil if desired.