Combine first 7 ingredients and 2 teaspoons oil in a small bowl; rub over chicken. Heat 2 teaspoons oil in a large skillet coated with cooking spray over medium-high heat. Add chicken; cook 5 minutes on each side or until browned. Remove chicken from pan; set aside.
Place flour in a bowl; gradually add milk and wine, stirring with a whisk until blended. Add to skillet, scraping pan to loosen browned bits; bring to a simmer. Return chicken to pan; cover, reduce heat, and simmer 30 minutes or until chicken is done. Add mushrooms; cover and simmer 5 minutes. Remove chicken from pan; cover and set aside. Add cheese to skillet; cook 5 minutes or until cheese melts, stirring constantly with a whisk. Place 1/2 cup rice on each of 4 plates. Top each with 2 chicken thighs and 1 cup sauce. Garnish with oregano sprigs and cranberries, if desired.