1. Bring chicken broth and 4 cups water to a simmer in a large saucepan over low heat. Snap off and discard tough ends of asparagus. Cut into 2-inch pieces.
2. Sprinkle chicken with herbes de Provence and 3/4 tsp. salt.
3. Melt 2 Tbsp. butter with 1 Tbsp. olive oil in a Dutch oven over medium-high heat; add chicken, and sauté 5 to 6 minutes or until done. Remove chicken; cover and keep warm.
4. Melt remaining 1 Tbsp. butter in Dutch oven; add zucchini, onion, and asparagus, and sauté 3 minutes or until tender. Remove vegetables; cover and keep warm.
5. Sauté rice in remaining 1 Tbsp. hot oil in Dutch oven over medium-high heat 1 minute. Reduce heat to medium. Add wine and remaining 1/2 tsp. salt, and cook, stirring often, until liquid is absorbed. Add 1 cup hot broth mixture; cook, stirring often, until liquid is absorbed. Repeat procedure with remaining broth mixture, 1 cup at a time. (Total cooking time is about 30 minutes.)
6. Stir in grated cheeses, chicken, and vegetables until creamy. Stir in parsley and pepper. Serve immediately.