Place 1 tsp. of the ¼ cup granualted sugar into a large mixing bowl. Add the ½ c. warm milk and stir to combine. Sprinkle yeast across the top of the mixture and stir gently to combine. Let the mixture sit until it becomes frothy and bubbly (about 15 min.)
After mixture is frothy, add in the remainder of the sugar, ¼ c. warm milk, starter, bread flour, egg and salt.
Either by hand or with the paddle attachment of a stand mixer, mix until the dough is combined and raggedy looking. With a dough hook, knead dough for about 5-minutes on low speed. Divide the four tbsp. of butter into four parts and mix in one part at a time, combining for approximately 20 seconds after each addition. Then knead on medium speed for about 6-minutes, scraping the bowl occasionally. The dough should come together. Form the dough into a ball by hand and place in a large greased bowl, turning once to grease top of dough. Cover bowl with plastic wrap. Allow to rise in a warm place for about 1½ hours until doubled.
After dough has doubled, punch it down and turn it out onto a lightly floured surface. Roll to an 8x20 inch rectangle. Spread the filling across the top and top with the chocolate chips.
Starting at one long end, roll up the dough tightly, pulling back on the dough as you roll to keep the roll tight. Once rolled, seal the long edge seam by pinching the dough together with your fingers. Cut small amount off at each end to make even. Cut the roll into 10 equal pieces. They will probablay still be about 2-inches each because the dough will stretch a bit during rolling.
Place slices into a lightly greased 9x13 inch baking pan. Cover with plastic wrap and allow to rise in a warm place for about 1½ hours until doubled. After doubled, brush the rolls with the ¼ cup of reserved milk. This helps to brown tops.
Preheat oven to 350°.
Bake rolls on the center rack of your preheated oven for approx. 30 min. until lightly browned. Remove from oven and cool in pan on a wire rack until slightly warm. Using a writing tip and piping bag, ice across top of rolls. You can spread the icing on by hand if you choose or thin the icing by adding a little milk and spoon across the tops of the rolls.