Cut off ends of eggplant and slice into ⅓ inch rounds. Place a wire rack on a baking sheet. Lay the eggplant on the rack. Liberally sprinkle each side of the steaks with the salt and let the eggplant sit for 10 minutes. Rinse the eggplant under cool water and thoroughly pat dry with a towel.
Preheat oven to 400 F degrees. Line a large baking sheet with parchment paper. Arrange the eggplant and single layer on the parchment lined baking sheet. Brush both sides lightly with olive oil and a light sprinkle of black pepper.
Roast the eggplant in the oven for 10 minutes. Flip and roast for an additional 5 to 10 minutes.
While the eggplant is cooking, cut the polenta tube into 12 even rounds, season with black pepper. Heat 2 tablespoons of olive oil in a cast-iron skillet or heavy-bottomed saute pan. In batches, sear the polenta rounds until the polenta is golden brown on each side, about 4-5 minutes per side. Transfer to a serving platter.
Place all ingredients into a blender. Process on medium-high until mixture is smooth but grainy. Transfer to a small pan and heat on low heat until warmed through.
Layer the eggplant and polenta on a platter. Topped with the romesco sauce and arugula.
Polenta cakes can be made in advance and reheated in a frying pan.
Leftovers will keep in the fridge in a sealed container for 3 to 5 days.