Combine the first 5 ingredients in a medium bowl; stir well with a whisk.
Place the breadcrumbs in a shallow dish; dredge the chicken in breadcrumbs. Heat olive oil in a large nonstick skillet over medium-high heat; add the chicken, and sauté 6 minutes on each side. Remove chicken from pan. Add the carrot, onion, squash, zucchini, and vermouth to pan, and sauté 5 minutes, stirring occasionally. Return chicken to pan, and add the broth mixture. Bring mixture to a boil; cover, reduce heat, and simmer mixture 15 minutes. Serve chicken and vegetable mixture over the rice, and sprinkle with chopped rosemary.