Step 1

Preheat oven to 400°F.

Step 2

Cut delicata in half lengthwise; scoop out seeds and pulp. Cut lengthwise again, and then into 1/4-inch quarter-moons. Toss delicata in a medium bowl with 1 tablespoon oil, 1/2 teaspoon salt, and 1/4 teaspoon pepper until coated. Spread out in a single layer onto a large rimmed baking sheet. Roast, stirring once or twice, until tender and darkened in spots, 16 to 20 minutes.

Step 3

Meanwhile combine vinegar, honey, caraway, the remaining 3/4 teaspoon salt, and the remaining 1/4 teaspoon pepper in a microwave-safe measuring cup or bowl. Microwave until boiling-hot, 1 to 1 1/2 minutes. Remove from the microwave and stir in onion. Set aside for 10 minutes. Whisk in the remaining 2 tablespoons oil.

Step 4

Toss cabbage, apple, celery hearts, the hot roasted delicata squash, and the warm pickled onion dressing in a large salad bowl. Divide among four plates and top with walnuts and parsley (if using).