Melt teaspoon butter in a large skillet over medium heat. Add chicken to the pan; cook for 6 minutes, browning on both sides. remove the chicken from the pan; keep warm.
Add the remaining 2 teaspoons butter to the pan; swirl until the butter melts. Add the carrot, onion, celery, garlic, and dried plums; cook 4 minutes or until vegetables begin to soften, stirring frequently. Stir in thyme and sage; cook 30 seconds. Stir in mustard. Add the broth and 3/4 cup water, scraping pan to loosen the browned bits; bring to a simmer.
Return the chicken to the pan. Cover, reduce heat, and simmer for 35 minutes. Uncover, increase the heat to medium-high, and simmer until the sauce is reduced by half (about 10 minutes). Stir in salt and pepper. Serve over noodles.