In a large nonstick skillet, heat a drizzle of EVOO over medium-high heat. Add the chorizo and cook, turning, until brown and crisp on both sides, 4 to 5 minutes. Using a slotted spoon, transfer to a paper towel-lined plate to drain. Do not wipe out the skillet.
Trim the round ends off the polenta. Cut the log in half and cut each half into 4 equal rounds. Season both sides of each round with salt and pepper, add to the skillet and cook in the chorizo fat, turning, until golden brown and crisp on both sides, 12 to 15 minutes total. Transfer the polenta to another paper-towel-lined plate to drain.
Meanwhile, stir together the piquillo peppers and olives in a small bowl. To serve, place the crisp polenta rounds on a platter, top with about 1 teaspoon pepper-olive mixture and garnish each with a piece of chorizo and cilantro leaves.