1. Preheat broiler. Whisk together oil and 1-1/2 teaspoons cumin in a small bowl; salt to taste. Lightly brush both sides of each tortilla with cumin oil and arrange in a single layer on a cookie sheet. Broil 4 inches from heat, turning once, until golden brown and crisp, about 2 minutes. Transfer to rack to cool.
2. Meanwhile, toss chicken with 2 tablespoons juice in a serving bowl; salt and pepper to taste.
3. Toss together beans, tomatoes, 1 tablespoon juice, and remaining 1/2 teaspoon cumin in another serving bowl; salt and pepper to taste.
4. Halve, pit, peel, and slice avocado. Transfer to a shallow bowl and drizzle with remaining 1 tablespoon juice; salt to taste.
5. Arrange bowls of chicken, beans, avocado, and stack of tortillas on the table. Place lettuce, salsa, and sour cream in separate bowls; serve on the side with lime wedges. Top each tortilla with desired toppings to create individual salad tostadas. Makes 4 servings.