Making the dough: Mix 1 cup room temperature water with milk, yeast and sugar. Let stand for 5 minutes. In the bowl of a standing mixer combine flour and salt. Add butter and press it into the flour with your fingers to form small pieces (don't worry if it is not incorporated evenly). Add the yeast mixture and 1 egg to the bowl. Using the dough hook attachment, turn the mixer on low. Mix for 1 minute on low and then increase the mixer to 3/4 of its maximum speed. Keep mixing at this speed until dough comes together and slaps the sides of the bowl, about 5 minutes. The dough will be very loose and will fall back into the bottom of the bowl when the mixer is turned off. Remove the bowl from the mixer, cover the top with plastic wrap and allow to rise at room temperature until doubled in size, about 2 hours.

Preheat oven to 350. Line a baking sheet with parchment paper. Combine the chicken, barbecue sauce and onion in a small bowl and mix well. In another small bowl, lightly beat the remaining egg and set aside.

Forming the rolls: Dust a work surface with flour. Using lightly floured hands, remove 1/4 of the risen dough and gently roll it into a cylinder, approximately 8 inches long. (The dough will be quite sticky, but add only as much flour as you need to prevent it from sticking to your hands.) Using a knife or dough scraper, cut the cylinder of dough into 8 even pieces. Flatten each piece into a circle. Drop 1/2 teaspoon of the chicken mixture into the center of each dough circle. Pull the sides of the dough around the filling and twist them together firmly to seal the chicken inside. Place each filled roll, seam-side down on parchement paper. Brush the top of each roll liberally with the beaten egg.

Bake until the surface of the rolls are golden brown, 18-20 minutes. Serve warm or at room temperature.