In bowl of stand mixer, mix together the starter, milk, sugar, yeast, and about 1 cup of the flour. Let stand for about five minutes to allow the starter and yeast to start working. After about five minutes the mixture should look spongy and bubbled up. Add egg, 1/2 cup melted butter, and salt and mix together. Start adding the flour about a cup at a time until a soft dough forms and it starts climbing up the dough hook (this may not take all four cups or it might take more). It should still be slightly sticky but able to hold its shape. Remove dough to a floured surface and knead for a couple minutes to bring the dough together. Place in a slightly greased bowl and cover. Place in a warm place and allow the dough to double in size.
After dough has doubled in size (about and hour), punch it down and place on your lightly floured work surface. Roll dough into a square about 1/4 to 1/3 inch thick. Spread remaining 1/2 cup melted butter on the dough and sprinkle with the sugar and cinnamon. Roll dough up tightly and gently pinch the seam together. With a sharp knife, I used a serrated blade, trim the edges and cut log into eight even pieces. Place the cut rolls in a greased 9" by 13". Cover and let rise about 45 minutes until they have not quite doubled in size. Preheat your oven to 375 degrees and bake for about thirty five minutes until golden brown (until an instant read thermometer reads 190 to 200 degrees). Remove from oven and let cool about twenty minutes and frost.