Preheat a grill to medium high. Soak 8 wooden skewers in water, about 15 minutes. Meanwhile, make the dressing: Mix the olive oil, vinegar, oregano, shallot, garlic, red pepper flakes and 1 1/4 teaspoons salt in a large bowl. Drizzle the cut sides of each piece of romaine with about 1 teaspoon of the dressing. Add the chicken to the bowl with the remaining dressing and toss. Add the breadcrumbs and toss to coat. Thread the chicken onto the skewers, leaving space between each piece. Grill the chicken skewers, turning occasionally, until cooked through, 8 to 10 minutes. Meanwhile, grill the romaine, turning once, until marked and slightly wilted, 1 to 2 minutes. Transfer the romaine to plates and drizzle with olive oil and vinegar. Season with salt. Serve with the chicken skewers and sprinkle with the parmesan.