Preheat oven to 350 degrees and line a baking sheet with parchment paper.
Place your sliced eggplant on a cutting board and sprinkle with salt.* Allow to sit until the oven is done preheating. Wipe the salt (and the liquid released) off of the eggplant slices with a paper towel or clean kitchen towel. Place them on the baking sheet and drizzle with olive oil, salt & pepper. Place in the oven for 20 minutes, flipping halfway.
While the eggplant is cooking, prepare the pesto mayo. Combine the arugula, basil, walnuts and garlic in a food processor. Pulse until combined, scraping down the sides as needed. Add the olive oil, lemon juice, salt & pepper and pulse until smooth. Taste and adjust as needed. Spoon the pesto into a bowl and add the mayo. Stir to combine and place in the fridge until ready to use.
To assemble the sandwiches. Spread a layer of pesto mayo on 4 slices of bread. Top with roasted red peppers, arugula and eggplant. Top with remaining slices of bread - you can add another layer of pesto mayo to the top slice of bread too, if you're feeling adventurous. Serve and enjoy!
Notes
*The salt releases the moisture from the eggplant.