Place chicken, skin side up, in a single layer on vegetables; pour juices that have accumulated on plate into pot. Tie parsley sprigs, thyme sprigs, and bay leaf together with kitchen twine; add to pot. Bring to a boil, then reduce to a simmer. Cover partially. Cook until internal temperature of thickest part of chicken registers 165 degrees, 25 to 30 minutes. Transfer chicken to a clean plate. Simmer liquid, uncovered, until reduced slightly, about 5 minutes. Discard herbs.