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.
Herbes de Provence can be found online (try mccormick.com) or at Whole Foods Market.