5. Drizzle the apple slices with 1 tablespoon oil and turn to coat. Spread the apple slices in a single layer on the grill pan and cook over direct medium heat, with the lid closed, until they have grill marks on both sides, 4 to 6 minutes, turning once or twice. Remove the grill pan with the apples from the grill and transfer the apples to a cutting board. When cool enough to handle, cut the apples into 3/4-inch pieces. Lightly brush the romaine with oil, season evenly with salt and pepper, and then grill, cut side down first, over direct medium heat, with the lid closed, until slightly wilted, about 2 minutes, turning once. Transfer the romaine to a serving platter cut side up.
6. In a bowl combine the walnuts, apples, fennel, and cranberries. Pour in half of the dressing and toss to combine, adding additional dressing, if desired. Spoon the apple mixture over the romaine. Garnish with the tarragon and serve right away.