Slice the eggplant into ½” pieces. Arrange onto a paper towel lined baking sheet and sprinkle with salt. Let rest for 30 minutes to draw out excess moisture.
Meanwhile, prepare the sauce. Heat a frying pan as well as a small saucepan over medium high heat.
Pour the vodka into the saucepan and cook for 5 minutes to burn off the alcohol.
Meanwhile, add a tbsp of olive oil to the frying pan and swirl to coat the pan. Saute the onions for 5 minutes, turn off the heat and stir in the vodka. Grate 2 garlic cloves over the onions .
Next, combine the diced tomatoes, crushed tomatoes, basil, remaining garlic cloves, pepper, and salt in a food processor or blender and purée. Pour into the frying pan. Set the heat to a simmer and stir in the heavy cream. Cover and let simmer for 10 minutes.
Preheat the oven to 400 degrees F.
Combine olive oil, chopped basil, minced garlic, Italian parsley, dried oregano, red pepper flakes, pepper, and salt in a small bowl. Whisk well.
Remove eggplants from the paper towel and onto a wooden cutting board. Brush the eggplant and mozzarella slices with this mixture.
Discard the paper towel and add eggplants back to the baking sheet. Place into the oven and bake for 10 minutes.
Pour ½ cup of sauce onto the bottom of a casserole dish. Spread to cover.
Arrange eggplant and mozzarella slices in an alternating pattern starting from the outer edge of the pan to the middle.
Pour remaining sauce over the slices. Cover with parmesan and mozzarella cheese. Sprinkle with Italian seasoning and place into the oven. Bake for 20 minutes.
Garnish with chopped basil.