In a food processor fitted with a steel blade, process pepper and garlic until minced. Add oil, lemon juice and cumin, processing until mixed. Add the tomato and yellow pepper and chop coarsely. Transfer the tomato mixture to a large bowl. Place the jicama and parsley in food processor work bowl and chop coarsely. Add the jicama mixture to the tomato along with the rice and toss to thoroughly combine. Adjust seasoning.
To assemble: Peel avocados and cut into 1/2 inch cubes. Mix the avocados and cheese into the salad. Check seasoning and serve garnished with additional parsley. 4 servings.