In a medium saucepan, bring broth, water, and garlic to a boil. Add lentils and rice, reduce heat to medium-low, and simmer, covered, for 15 minutes. Add carrots and continue cooking, covered, for 7 to 8 minutes, or until most of the liquid is absorbed. Remove from heat.
In a large bowl, whisk together oil and vinegar. Add apple, onions, and parsley. Add lentil mixture, tossing to coat. Gently fold in cheese and pecans.
Divide spinach among four serving plates and spoon the salad on top. Garnish with apple slices and pecans.
*Available at health-food stores.