While the dough is rising, mix the cooled mushrooms and onions together in a bowl. Add the goat cheese and mix well.
Prepare a baking pan (we used a 9-inch cake pan) with edges by lining the bottom with parchment paper.
Fold the dough inwardly until all the air is knocked out from the dough. Roll out the dough into a 2-inch diameter log. Cut the log into 15 evenly sized pieces. Roll each piece out flat into a 3-inch diameter circle.
Fill each circle with the filling, about 1-2 tbsp in each bun, and bring the edges together and pinch together. Roll each piece into a ball, being careful to not let the dough tear. Arrange the balls into the prepared baking pan in concentric circles with the pinched side down, leaving about a ¼-inch between the balls.
Cover the pan and let the dough rest for about an hour.
About 20 minutes before you’re ready to bake the buns, preheat the oven to 350 F.
Right before baking, brush the tops of the buns with milk and sprinkle with sesame seeds. Bake the buns for 25-30 minutes or until the tops of the buns are golden brown. Serve warm.