Place the dough in the bowl of an electric mixer fitted with the dough hook, add the softened butter in chunks, and mix for 2 minutes, adding additional flour as needed to make a ball. Turn the dough onto a lightly floured board and divide the dough into 20 (1 3/4-ounce) balls and place them in the tins. Cover the tins with a damp towel and set aside to rise at room temperature until doubled in volume, about 2 hours.
04Preheat the oven to 350 degrees F. When the rolls have risen, brush the top of each with the egg wash and bake for 20 minutes, or until the tops spring back and it sounds slightly hollow when tapped. Turn the rolls out onto a wire rack to cool.