Set a large skillet over high heat with the butter and oil. Once melted, add the chicken all at once. Cook until browned on all sides, stirring often, about 10 minutes. Remove chicken with a slotted spoon to a plate or platter.
Add the onions, garlic, and mushrooms and cook until caramelized and brown, about 8 minutes. Sprinkle the flour on top and stir to fully combine. Cook for about 1 minute. Reduce the heat to low, and stir in the half and half. Bring to a simmer and cook until thickened, about 5 minutes. Season with salt, pepper, and paprika and add the chicken back in. Cook for another 3 to 5 minutes. Garnish with parsley and serve on top of white fluffy rice.