Slice the chicken breast in half horizontally to make 2 thin cutlets; season with salt and pepper. Heat 1/2 tablespoon olive oil in a large nonstick skillet over medium-high heat. Add the chicken and cook until lightly golden and cooked through, 4 to 5 minutes per side. Transfer to a plate to cool, then thinly slice.
Meanwhile, combine the cranberries, vinegar and 1 tablespoon water in a small microwave-safe bowl. Cover with plastic wrap and microwave 45 seconds to plump the cranberries. Let cool.
Whisk the cranberry-vinegar mixture, lemon juice, mustard, 1/2 teaspoon salt, and pepper to taste in a large bowl. Whisk in the remaining 3 tablespoons olive oil in a slow stream until blended. Add the chicken, spinach, endives, almonds, pear, about half of the cheese, and salt and pepper to taste; toss to combine. Divide among bowls and top with the remaining cheese.