Heat the oil in a large deep saute pan over a medium heat.
Season the chicken thighs generously with salt and pepper and place skin-side down in the pan with the lemon zest, thyme and potatoes.
Allow the chicken thighs and potatoes to cook without moving for 10 to 15 minutes, or until the chicken skin turns crisp and a deep golden brown color. Turn the chicken and potatoes, add the carrots and cook for 2 to 3 minutes until the carrots are starting to become tender.
Combine the chicken stock and mustard, then add to the pan. Bring to a simmer, then add the kale. Season, cover and cook for 10 minutes more until the chicken is cooked all the way through, the potatoes and carrots are tender and the liquid has reduced slightly.
Serve straight to the table with a good squeeze of lemon juice and a generous sprinkling of parsley.