Preheat oven to 450°. Place potatoes in a medium saucepan; cover with water. Bring to a boil, and simmer 12 minutes or until tender. Drain. Heat a large ovenproof skillet over medium-high heat. Add 1 teaspoon oil to pan. Sprinkle chicken with 1/4 teaspoon salt and 1/4 teaspoon pepper. Add chicken and thyme sprigs to pan; cook 5 minutes or until chicken is browned. Turn chicken over. Place pan in oven; bake at 450° for 10 minutes or until chicken is done. Remove chicken from pan. Return pan to medium-high heat. Add remaining 2 teaspoons oil. Add potatoes, cut sides down; mushrooms; and 1 tablespoon thyme; cook 3 minutes or until browned, stirring once. Combine milk and flour in a small bowl, stirring with a whisk. Add remaining salt, remaining pepper, flour mixture, stock, lemon, and beans to pan; simmer 1 minute or until slightly thickened. Add chicken; cover, reduce heat, and simmer 3 minutes or until beans are crisp-tender. Sprinkle with parsley.