Season and bake chicken breasts in a 350 degree oven until no longer pink in center. Dice chicken and set aside.
Roll out a handful of bread dough into a 1/4 inch thick rectangle. Spread 1-2 tsp of softened cream cheese over dough. Add 1-2 Tbsp of alfredo sauce over the cream cheese. Top with 1/2 cup diced chicken, 1/4 cup steamed chopped broccoli, and 1/4 - 1/3 cup cheddar cheese.
Fold up ends of dough over the filling mixture. Fold other ends up and over and seal seams shut using a bit of water if necessary.
Place seam side down on a prepped baking sheet, cut a small steam vent in the top, and let rise for about 30 minutes in a warm, draft-free place.
Bake at 400 degrees until golden brown, about 20-25 minutes. Brush with oil mixture again after baking if desired.