1. Heat the oil in a large skillet over medium-high heat. Working in batches to avoid overcrowding the skillet, add the chicken to the skillet; cook, stirring occasionally, until golden and no longer pink in the center, about 6 minutes. Transfer chicken to a plate.
2. Reduce the heat to medium. Add the mushrooms to the skillet; cook until the mushrooms release their juices and are golden and tender, about 6 minutes. (If the skillet becomes too dry, add 1 or 2 teaspoons of the chicken broth, or more as needed.)
3. Meanwhile, stir together the flour and 2 tablespoons of the milk in a measuring cup until the mixture is smooth and no lumps remain. Stir in the remaining milk until well blended.
4. Return the chicken to the skillet. Increase the heat to medium-high. Add the chicken broth to the skillet.
5. Stir flour mixture, salt, paprika and black pepper into skillet. Bring to boiling. Reduce heat to medium; simmer, stirring occasionally, until mixture thickens slightly, about 5 minutes. Serve with hot cooked rice.