Preheat the oven to 350 degrees F.
For the eggplant parm: Dredge the eggplant slices in flour, then in egg, then in breadcrumbs, shaking off excess at each step. Heat the olive oil, butter and garlic in a large skillet. Working in batches, pan-fry the eggplant until golden brown on both sides. Add more olive oil, butter and garlic as needed for each batch. Remove and replace any garlic cloves that begin to look scorched. Transfer the eggplant to paper towels to cool. Season with salt.
Lay a single, even layer of eggplant in a 9-by-13-inch springform pan, making sure to cover the entire surface of the pan. Spread 8 ounces of tomato compote evenly over the eggplant. Sprinkle generously with Parmesan, then layer with sliced mozzarella and torn basil leaves.
Add another layer of eggplant, again laid out evenly and covering all surfaces. Spread another 8 ounces of tomato compote over the eggplant. Sprinkle generously with Parmesan and torn basil leaves. Add a third layer of eggplant, followed by 8 ounces of tomato compote, another generous sprinkling of Parmesan, a second layer of mozzarella and a scattering of torn basil leaves.
Add a fourth layer of eggplant, yet another 8 ounces of tomato compote and more Parmesan and torn basil leaves. Cover with plastic wrap and foil and bake for 45 minutes. Let cool completely before removing from the springform pan
Slice into 14 pieces. Re-heat and serve with tomato compote and grated Parmesan.