Wash the eggplant, peel it, and cut it lengthwise.
For the basil butter, make sure the butter is soft at room temperature. Add ½ cup of basil pesto to a bowl with the softened butter and mix until incorporated and smooth. Set aside.
To bread the eggplant, break the eggs in a large bowl, add a pinch of salt, and whisk. Prepare a baking tray or a large plate with the breadcrumbs—season with salt and pepper.
Add the eggplant to the eggs, coat them very well, and then move them into the breadcrumbs. Cover the slices and pat them to ensure they get an even layer of breadcrumbs. Turn and repeat.
Heat the frying oil to 350F. When ready, fry the eggplant a few slices at a time so you don’t overcrowd the pan and drop the oil temperature.
Fry for a few minutes on each side until golden brown. Move to a tray with paper towels to get rid of excess oil. Season with salt when hot.
Toast the bread in a sauté pan/cast iron with some olive oil. Get the pan hot, drizzle a little olive oil, and then place the bread in the pan. Cook until golden brown and flip.
Now, to assemble your sandwiches spread the basil butter on the bottom slice of bread, lay the pepper bruschetta (approx. ¼ cup per sandwich) on top of the pesto, then a couple of slices of eggplant. Cover with the mozzarella broken with your hands and a few slices of fresh basil. Spread the top slice of bread with 1 tablespoon of Dijon mustard per sandwich.Buon appetito!