How to Make It
Preheat oven to 425°F. Stack tortillas; cut in half, and cut crosswise into 1/2-inch strips. Place tortilla strips on a rimmed baking sheet. Toss with cumin, 1 tablespoon of the olive oil, and 1/4 teaspoon of the salt. Spread strips in a single layer; bake in preheated oven until golden brown and crisp, 10 to 12 minutes, turning halfway through baking. Cool strips to room temperature.
Meanwhile, whisk together lime zest, lime juice, shallot, apple cider vinegar, Dijon mustard, honey, pepper, and remaining 1/3 cup oil and 3/4 teaspoon salt until well combined. Set aside.
Toss together chopped chicken, avocado, romaine, sliced radishes, and Pickled Red Onions in a large bowl. Add 6 to 7 tablespoons vinaigrette; toss to coat. Place 2 cups salad on each of 4 plates; top each with 3 baked tortilla strips. Serve with remaining vinaigrette.