1. Preheat oven to 450°.
2. Combine first 5 ingredients in a small saucepan; bring to a boil. Cook until reduced to 1/3 cup (about 20 minutes). Strain cider mixture through a sieve into a bowl; discard solids.
3. Brush olive oil on a baking sheet; arrange endive halves, cut side down, on prepared pan. Brush 2 tablespoons cider mixture over endive; sprinkle with 1/8 teaspoon salt and 1/4 teaspoon pepper. Bake at 450° for 10 minutes. Remove from oven; turn endive halves over. Brush cut sides with 2 tablespoons cider mixture.
4. Preheat broiler.
5. Broil endive 4 minutes or until edges begin to brown.
6. Combine remaining 1/4 teaspoon salt, remaining 1/4 teaspoon pepper, remaining cider mixture, lemon juice, and walnut oil in a large bowl, stirring with a whisk. Add arugula, walnuts, and pear, tossing to coat. Arrange 2 endive halves on each of 4 salad plates, and top each serving with 1 1/2 cups arugula mixture.