Place potatoes in a pot, cover with water, bring to a boil and season with salt. Cook until almost tender; add green beans and cook 3 minutes more. Drain, return everything to the hot pot and cover.
Meanwhile, heat EVOO in a large saut pan over medium-high heat. Season chicken on both sides with salt and pepper, and cook 10-12 minutes, turning once. Remove to plate.
Add butter to the pan, melt and brown butter until golden and nutty in aroma. Whisk in flour, cook 1 minute then add stock and thicken to coat spoon. Add honey, parsley and mustard. Add cooked chicken and turn to coat; simmer a minute or 2 to heat through and transfer to a serving platter. Add potatoes and beans to the pan and turn them in the remaining sauce. Plate alongside chicken on the serving platter.