Preheat grill or broiler. Place cactus paddles in a bowl and toss with 1/4 cup of the olive oil and 1/2 teaspoon of the salt. Grill or broil the paddles until grill marks appear on each side, or they turn dark green with black patches, about 3 to 5 minutes. Set aside to cool to room temperature. Cover and chill 2 to 4 hours or overnight. Cut cactus into 1/2-inch pieces. In a large bowl, combine the cactus, tomatoes, onions, chiles, cilantro and cheese with the remaining 1/2 cup oil, the vinegar, the remaining 1 teaspoon salt and pepper. Toss well. Serve on plates lined with lettuce leaves, and garnish with avocado slices sprinkled with cracked pepper garnish.
In a small bowl, stir all the ingredients together. Spoon over vegetables or drizzle lightly over dressed salads as a garnish.
c.1997, M.S. Milliken & S. Feniger, all rights reserved