Place a large deep-sided skillet (or pot) over medium heat and add the butter. Once melted, brown the chicken in two batches until there is a nice sear on the skin. (It will finish cooking later.) Transfer the chicken to a plate and set aside.
In the same skillet, cook the onions for about 3-5 minutes until softened. Then add in the garlic and Roma tomatoes and cook for another 3-5 minutes, stirring often to prevent the garlic from burning.
Take the pan off the heat. Stir in the paprika, salt, and black pepper until well combined. (Paprika is very heat sensitive and can burn quickly, so be sure to add it off the heat.)
Add the chicken back to the skillet, along with enough chicken broth to almost cover the chicken. Bring things to a boil, then reduce to a low boil. Cover and cook for 40 minutes.
Once the chicken is done, remove it once again to a plate. Then whisk the sour cream and heavy cream together in a small bowl. Whisk in the flour until there are no lumps. Pour this mixture into the skillet and whisk consistently to prevent lumps. Cook the sauce down until it starts to thicken slightly, about 15 minutes.
Add the chicken back to the sauce and cook until it's warmed through. Garnish with chopped parsley and serve warm over cooked egg noodles, spaetzle, or with mashed potatoes.
Notes
In the US, spices labeled "paprika" almost always use sweet paprika. So you can just get a jar of McCormick paprika or the store brand and you'll be all set. Hungarian paprika (without the word "sweet") is also the same thing.
Nutritional information is for 2 chicken thighs and 1/4 of the sauce in the skillet.