Preheat oven to 375°. Pat chicken thighs dry with a paper towel and season on all sides with salt and pepper.
Heat 1 tbsp olive oil in a large skillet over medium heat. Add chicken to skillet skin-side-down. Cook, undisturbed, for 6-7 minutes until skin is golden brown. Remove to a plate.
Without wiping out the pan add the shallot, celery, bell pepper, broccoli, carrot, rosemary, thyme, 1/2 tsp salt and 1/4 tsp pepper. Cook, stirring occasionally, for 8-10 minutes until vegetables are starting to brown and soften. Add flour and cook for 1 minute while stirring. Mix in rice, chicken stock, milk, and zest from lemon. Bring to a low boil then remove from heat.
Add chicken skin-side-up on top of rice mixture. Transfer to oven for 20-25 minutes. Remove from oven when liquid has mostly absorbed, rice is tender, and chicken is 160-165°. Remove chicken and stir parsley and Parmesan cheese into rice. Season to taste with lemon juice, salt, and pepper. Serve rice topped with chicken.