Season both sides of the chicken thighs with salt and pepper.
In a large skillet or dutch oven over medium-high heat, sear the chicken on each side for 3-5 minutes, or until browned, but not completely cooked. It may have to cook in batches. Remove from heat and set aside, leaving any drippings in the pan.
Add in 2 tablespoons of the butter. Once melted, add in the onion and cook until tender, about 3-5 minutes.
Add in the garlic and frozen broccoli. Lightly season with salt and pepper, then cook for another 2-3 minutes.
Stir in the flour, paprika, thyme, parsley, and red pepper flakes. Cook for 1 more minute.
Pour in the chicken stock and scrape off any bits stuck to the bottom of the pan.
Mix in the soup and remaining tablespoon of butter.
Bring to a boil. Then add in the half-and-half and the rice.
Reduce the heat to low and cover the pan with a lid, leaving a small crack for steam to escape.
Cook on low for 18 minutes.
After 18 minutes, uncover the pan and stir in the cheese and the juice of 1 lemon wedge.
Season with salt and pepper if needed before serving.