1. FOR THE DOUGH: Adjust an oven rack to the middle position and heat the oven to 200 degrees. When the oven reaches 200 degrees, shut it off. Line a 13x9" baking pan with foil, allowing the excess to hang over the pan edges. Grease the foil and a medium bowl.
2. Whisk the milk and yeast in a liquid measuring cup until the yeast dissolves, then whisk in the eggs. In the bowl of a stand mixer fitted with the dough hook, mix the flour, cornstarch, granulated sugar, and salt until combined. With the mixer on low, add the warm milk mixture in a steady stream and mix until the dough comes together, about 1 minute. Increase the speed to medium and add the butter, 1 piece at a time, until incorporated. Continue to mix until the dough is smooth and comes away from the sides of the bowl, about 10 minutes. If the dough is still wet and sticky after mixing for 10 minutes, add up to 1/4 cup flour (1 tablespoon at a time) until the dough releases from the bowl. Turn the dough out onto a clean surface and knead to for m a smooth, round ball. Transfer the dough to the prepared bowl, cover with plastic wrap, and place in the warm oven. Let rise until doubled in size, about 2 hours.
3. FOR THE FILLING: Combine the brown sugar, cinnamon, and salt in a small bowl. Turn the dough out onto a lightly floured counter. Roll the dough into an 18-inch square, spread with the butter, and sprinkle evenly with the brown sugar mixture. Starting with the nearest edge, roll the dough into a tight cylinder, pinch lightly to seal the seam, and cut into eight pieces. Transfer the pieces, cut side up, to the prepared pan. Cover with plastic wrap and let rise in a warm spot until doubled in size, about 1 hour. (After transferring the pieces to the prepared pan, the buns, covered with plastic wrap, can be refrigerated for up to 24 hours. When ready to bake, let sit at room temperature for 1 hour. Remove the plastic wrap and continue with step 4 as directed.)
4. FOR THE GLAZE AND TO BAKE: Heat the oven to 350 degrees. Whisk the cream cheese, milk, vanilla, and confectioners' sugar in a medium bowl until smooth. Discard the plastic wrap and bake the buns until deep golden brown and the filling is melted, 35 to 40 minutes. Transfer to a wire rack and top the buns with 1/2 cup of the glaze; let cool for 30 minutes. Using the foil overhang, lift the buns from the pan and top with the remaining glaze. Serve.