In a 2- to 3-quart pan over high heat, bring about 1 quart water to a boil. Add asparagus and cook until crisp-tender, 2 to 3 minutes. Drain, then plunge asparagus into ice water to stop the cooking. Drain and set aside.
Cut off and discard ends from oranges. Following the curve of the fruit, cut off peel and outer membrane. Slice oranges crosswise into 1/4-inch-thick rounds, then cut these rounds into quarters. Set aside.
Pour the vegetable oil into a 3- to 4-quart pan (the oil should be about 1/2 inch deep) and set over medium-high heat. When oil reaches 350°, add wonton strips and fry, stirring, until golden brown on both sides, about 30 seconds total. Lift out with a slotted spoon and transfer to paper towels to drain.
In a large serving bowl, toss the cabbage, chicken, and asparagus with the dressing. Top with avocado, orange slices, and wonton strips, then garnish with green onions and sesame seeds.
Spicy soy-ginger dressing. In a medium bowl, whisk together 2 tablespoons rice wine vinegar, 2 tablespoons brown sugar, 1 1/2 tablespoons soy sauce, 1 tablespoon Asian red chile sauce (such as Sriracha), and 1 1/2 teaspoons grated fresh ginger. Slowly drizzle in 1/4 cup vegetable oil or grapeseed oil, whisking constantly. Season with salt to taste.
Note: Nutritional analysis is per serving.
Notes: To save time, you can use store-bought crispy wontons or chow mein noodles instead of frying your own. You can also substitute one 11-ounce can of mandarin oranges for the fresh orange slices.