Pour the warm water into a large mixing bowl and stir in the yeast and sugar. Let sit until foamy, about 3-5 minutes. Stir in the oil, salt and 1 cup flour until combined. Continue adding and mixing in the flour until dough is smooth and no longer sticky. Knead (or beat with a dough hook in a mixer) for an additional minute. Cover and let rise for one hour.
Season the chicken with salt and pepper to taste. Cook in the microwave until fully cooked, about 8-10 minutes. Or, bake in a 375 degree oven for 20-30 minutes, until fully cooked. Cool completely and refrigerate until using.
Beat together the softened cream cheese and hot sauce until smooth. Cube or shred the cooled chicken and stir in to the cream cheese mixture. Adjust the amount of hot sauce used per your tastes. Refrigerate until using.
Roll out the dough on a well floured surface. Cut into circles with a small biscuit cutter or juice glass. Place about a teaspoon of the buffalo chicken filling in the center of each circle and fold the dough over to close. Press to seal lightly. Place the finished puffs on a baking sheet.
Melt the butter and brush over each puff. Bake at 375 degrees for 15 – 20 minutes, until lightly golden brown. If desired, serve with celery sticks and Ranch or Bleu Cheese dressing for dipping.