Create a dry rub for the chicken by combining lemon pepper, garlic salt, and paprika in a bowl. Sprinkle the rub over both sides of the chicken and lightly pat.
In an oven-proof pot, warm olive oil on medium heat. Place each chicken thigh in the oil, skin-side down. Cook for 3-4 minutes, then turn up heat to medium high and cook for another 2-3 minutes. Then turn the chicken over one more time and cook for another 3-4 minutes. The chicken should be fairly browned, though not fully cooked. It will finish cooking in the oven. Remove the chicken from the pot and set aside.
Add 2 tablespoons butter to the pot and melt over medium-high heat. Saute the garlic in the butter for about a minute. Pour in the rice and saute for 2-3 minutes.
Pour in 1/4 cup chicken broth and 2 tablespoons lemon juice. Cook for another couple minutes before pouring in the rest of the chicken broth. Add one cup of milk and salt and pepper. Stir and bring to a simmer.
Return the chicken to the pot amid the chicken. Place the lid on the pot and bake at 350 degrees for 20 minutes.
Remove the lid and continue to cook another 10 minutes.
Remove the chicken and place on a baking sheet. Broil on high for 2-3 minutes, browning the skin.
Finish the rice by stirring in 2 tablespoons butter, Parmesan cheese, and 1/2 cup milk. Stir until well combined. Top with parsley.
Serve the chicken on a bed of rice.