Warm the Greek yogurt and milk together in the microwave for 30 to 45 seconds until slightly warm but not hot. If the mixture is too hot it can affect your starter.
In a large bowl whisk together the bread flour, baking powder, salt, and sugar. In a separate bowl whisk together the starter, warmed yogurt and milk mixture, vanilla extract, and eggs until smooth, then mix in the softened butter.
Pour the wet mixture into the dry ingredients and mix until a soft, slightly tacky dough forms.
Knead the dough on a lightly floured surface or in a stand mixer with the dough hook for 5 to 6 minutes until smooth and elastic, aiming for a partial windowpane. The dough will feel softer and more relaxed than a lean sourdough, which is correct for an enriched dough.
Place the dough in a lightly oiled bowl and cover. Perform one set of stretch and folds after the first 30 to 45 minutes, then leave it alone. Bulk ferment at room temperature for 6 to 10 hours until the dough has increased 50 to 75 percent in volume and looks domed and jiggly. At 65 degrees Fahrenheit this can take up to 12 hours overnight.
While the dough ferments, make the filling. Using a stand or hand mixer, whip the room temperature butter on medium speed until pale and fluffy, about 60 seconds. Add both sugars, the cinnamon, and cornstarch and mix on medium until a thick uniform paste forms. Set aside at room temperature.
Turn the dough out onto a lightly floured surface and gently roll into a rectangle 12 inches wide by 18 inches tall with the 12 inch edge parallel to your body. If the dough springs back, let it rest for 5 minutes and try again.
Spread the filling evenly over the entire surface of the dough going edge to edge on the short sides and leaving a half inch border along the far long edge. Work in small dollops first then connect them with an offset spatula using short strokes from the center outward.
Starting from the 12 inch edge closest to you, roll the dough upward and away from you into a tight log, pressing gently as you go. Pinch the seam firmly to seal. The log will be approximately 12 inches long.
Using unflavored dental floss, trim any uneven ends off the log first, then cut into 12 equal rolls at 1 inch each. Run the floss under the log, cross the ends over the top, and pull tight for a clean cut.
Arrange the rolls cut side up in a lightly greased or parchment lined 9x13 pan with a little space between each. Cover and proof at room temperature for 3 to 4 hours until the rolls are puffed and touching each other and pass the poke test. Press gently with one finger and the dough should spring back slowly, leaving just the faintest impression.
Preheat the oven to 375 degrees Fahrenheit. Brush the tops of the rolls gently with egg wash. Bake for 25 to 30 minutes until deep golden brown. The center of a middle roll should read 190 degrees Fahrenheit on an instant read thermometer.
While the rolls bake, beat together the cream cheese and butter until smooth. Add the sifted powdered sugar, vanilla, salt, and enough milk to reach a smooth, pourable consistency. Add additional powdered sugar up to 120 grams more if you prefer a thicker icing.
Let the rolls cool in the pan for 10 minutes, then pour or spread the cream cheese glaze generously over the top. Serve warm.