Combine 1 cup flour, undissolved yeast, sugar and salt in a large bowl. Add very warm water and oil; mix until well blended, about 1 minute. Gradually add enough remaining flour to make a soft dough. Dough should form a ball and will be slightly sticky. Knead** on a floured surface, adding additional flour if necessary, until smooth and elastic, about 4 minutes. Cover and let dough rest for 10 minutes.
While dough is resting, in a large bowl, mix chicken, Cheddar-Monterey cheese, cream cheese and buffalo sauce. Set aside.
On a floured surface roll dough out to 14x12-inch rectangle and cut into 24 squares. Place 1 tablespoon of the chicken mixture on the center of each square. Pull corners together to enclose filling; pinch to seal. Place in a greased pie or square 9x9-inch dish, sealed side down.
In a small bowl mix the Parmesan cheese and dried ranch dressing mix together. Brush tops with the butter, sprinkle with Parmesan cheese mixture. Bake on lowest oven rack for 25 to 30 minutes.
*If you don't have a thermometer, water should feel very warm to the touch.
**To knead the dough, add just enough flour to the dough and your hands to keep the dough from sticking. Flatten dough and fold it toward you. Using the heels of your hands, push the dough away with a rolling motion. Rotate dough a quarter turn and repeat the "fold, push and turn" steps. Keep kneading dough until it is smooth and elastic. Use a little more flour if dough becomes too sticky, always working the flour into the ball of dough.