Make the whipped goat cheese: Add the goat cheese, olive oil, lemon juice, parsley, salt, and pepper to a food processor. Blend until smooth and creamy, scraping down the sides as needed. Set aside.
Prepare the cherry chimichurri: In a medium bowl, combine the chopped cherries, parsley, oregano, garlic, shallot, red wine vinegar, red pepper flakes, salt, and black pepper. Stir in the olive oil until well combined. Let the chimichurri sit for at least 15 minutes to allow the flavors to meld.
Cook the duck breast: Preheat oven to 375. Pat the duck breast dry with paper towels and score the skin in a crosshatch pattern, being careful not to cut into the meat. Season both sides with the salt and pepper.Place the duck skin-side down in a cold cast-iron skillet. Turn the heat to medium and cook for 7 minutes, allowing the fat to slowly render and the skin to become deep golden and crisp. Flip duck and cook for another minute. Render fat and flip duck to skin side down again. Transfer to the oven and cook for another 4-6 minutes depending on thickness of breast. Internal temperature should reach 130–135°F for medium-rare. Transfer to a cutting board and let rest for 5–10 minutes before slicing thinly (see note). Toast ciabatta: Lightly toast the ciabatta rolls until golden and crisp.
Assembly: Spread a generous layer of whipped goat cheese on both halves of each toasted ciabatta roll. Layer the sliced duck breast over the bottom half, then spoon plenty of cherry chimichurri over the duck. Close the sandwiches and serve immediately.