Add the butter and olive oil to a large skillet over medium-high heat and brown the chicken for 3-4 minutes per side. Transfer the chicken to a plate and set aside until needed.
Add the onions to the pan with the cooking oil and cook for 6- 8 minutes over medium heat until golden brown.
Add the garlic, diced bell peppers, and tomatoes to the pan and cook for 2-3 minutes.
Remove the pan from the heat and add the paprika, salt, and black pepper. Stir the seasonings in to combine.Don't let the paprika burn, it will get bitter. Return the chicken to the pan and place it back on the stovetop.
Add the chicken broth (most of the chicken should be covered) and turn the heat up to medium-high heat. Bring the mixture to a boil, cover, and reduce the heat to low. Simmer the mixture for 45-60 minutes.
Remove the chicken from the pot and transfer it to a plate. Tent with foil to keep warm.
Keep the sauce on the stove over simmering over medium heat to reduce and thicken the sauce. Stir the sauce to get all the tasty browned bits off the bottom of the pan.
Add the sour cream and heavy cream to a small bowl and whisk to combine.
Add the flour to the sour cream mixture and whisk to combine.
Add the sour cream mixture to the pot, constantly whisking to prevent lumps from forming. Bring the sauce back to a simmer and let it cook for 4 -5 minutes until the sauce has thickened.
Re-season the sauce with salt and pepper to taste. Return the chicken to the sauce, increasing the heat to medium, and let the chicken reheat for 5 minutes or until it's at least 165 degrees F.
Serve the chicken over egg noodles and garnish with chopped Italian parsley.