Brush eggplant rounds with 2 tablespoons vegetable oil. Place on a baking sheet.
Bake in the preheated oven until eggplants are soft and brown, about 15 minutes. Remove from oven. Keep oven on.
Heat 2 tablespoons oil in a saucepan over medium heat. Add onion and garlic; cook and stir until onion is translucent, about 5 minutes. Add tomatoes and tomato paste. Cook until flavors are blended, about 3 minutes. Stir in stock, basil, paprika, oregano, salt, and pepper. Cook until red sauce is thickened, about 15 minutes.
Melt butter in a saucepan over medium heat. Add flour; cook and stir until light brown, 6 to 10 minutes. Remove from heat. Add milk slowly, whisking constantly, until mixture is smooth, about 2 minutes. Return to heat. Bring to a boil, stirring with a wooden spoon. Cook and stir until bechamel sauce thickens and coats the back of the spoon, 5 to 7 minutes more. Remove from heat; stir in Parmesan cheese, garlic powder, salt, nutmeg, and white pepper.
Cover the bottom of a baking dish with 2 tablespoons of the red sauce. Arrange 1 layer of eggplant on top; cover with some mozzarella slices. Spread 3 to 4 tablespoons bechamel sauce on top. Repeat layering until you reach a final layer of bechamel sauce; top with remaining mozzarella.
Bake in the preheated oven until cheese melts and turns golden brown, 25 to 30 minutes.