Cut the chicken into long strips about 2 inches thick. Combine the olive oil, paprika, salt and pepper in a bowl, mix well. Place the chicken in a large food storage bag and pour the oil mixture over the chicken. Refrigerate for at least ½ hour, or up to 1 day.
Heat a large cast iron or non stick skillet over medium-high heat. Remove the chicken from the marinade and allow the excess olive oil to drip off. Carefully place the chicken in the heated skillet. Cook, turning occasionally until chicken is no longer pink. Turn heat to low, and prepare the sauce.
In a medium saucepan, melt the butter over medium heat. Add the minced garlic and saute for 1-2 minutes. Slowly stir in the half and half, then add the parsley, paprika, salt and pepper, heat through. Slowly add the shredded Gouda, stirring constantly, until all the cheese is melted. Reduce heat to low to keep warm.
Turn the heat back up on the chicken, and continue to cook, turning occasionally, until lightly browned and 180 degrees on a meat thermometer. Place the chicken on plates, then spoon the sauce over the top.