In a small bowl mix the thyme, paprika, pepper, salt, rosemary and 1 Tablespoon parsley. Season the chicken with the spice mix, using all of it to cover the thighs.
In a large pan, melt 2 tablespoons of butter over medium low heat, and place the thigh pieces in the pan. Cook one side for 5 to 6 minutes then flip them over and repeat until cooked through or thermometer reads 165 °F (74 °C). Remove chicken from pan and let rest.
Melt the remaining butter in the pan and add the shallots and garlic, cooking for 1 minute.
Add the broccoli, you can add the chicken broth at this time if you want to, or just steam the broccoli without broth, add the lid and allow to cook for 4 to 5 minutes till steamed.
Remove the lid and push the broccoli to one side leaving some of the onions and shallots on one side for the chicken.
Place the chicken back in the pan and using a spoon, baste with any remaining butter in the pan.
Turn off the heat and squeeze the lemon over the chicken and broccoli. Sprinkle the zest and parsley over the chicken and broccoli and serve.