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.
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.
Preheat broiler.
Broil endive 4 minutes or until edges begin to brown.
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.