Instructions

For the Dough: Adjust oven rack to middle position and heat oven to 200 degrees. When oven reaches 200 degrees, shut off. Line 13- by 9-inch baking pan with foil, allowing excess foil to hang over pan edges. Grease foil and medium bowl.
Microwave ¾ cup whole milk in liquid measuring cup until it registers 110 degrees, 30 to 60 seconds. Whisk in 2¼ teaspoons instant or rapid-rise yeast until dissolved, then whisk in 3 large room-temperature eggs.
In bowl of stand mixer fitted with dough hook, combine 4¼ cups (21¼ ounces) all-purpose flour, ½ cup (2 ounces) cornstarch, ½ cup (3½ ounces) granulated sugar, and 1½ teaspoons table salt. With mixer on low, add warm milk mixture in steady stream and mix until dough comes together, about 1 minute.
Increase speed to medium and add 12 tablespoons softened unsalted butter, one tablespoon at a time, until incorporated. Continue to mix until dough is smooth and comes away from sides of bowl, about 10 minutes.
Turn dough out onto clean surface and knead to form a smooth, round ball. Transfer dough to prepared bowl, cover with plastic wrap, and place in warm oven. Let rise until doubled in size, about 2 hours.
For the Filling: Combine 1½ cups packed (10½ ounces) light brown sugar, 1½ tablespoons ground cinnamon, and ¼ teaspoon table salt in small bowl. Turn dough out onto lightly floured surface. Roll dough into 18-inch square. Spread 4 tablespoons softened unsalted butter evenly over dough, leaving ½-inch border around edges. Sprinkle sugar mixture evenly over butter and then lightly press into dough.
Starting with the edge nearest you, roll dough into tight cylinder. Pinch lightly to seal seam. Use a knife to cut the rolled log in half and then cut each half into 4 equal pieces. Transfer pieces, cut-side up, to prepared pan. Cover with plastic wrap and let rise in warm spot until doubled in size, about 1 hour.
Heat oven to 350 degrees. Discard plastic wrap and bake buns until deep golden brown and filling is melted, 35 to 40 minutes.
For the Glaze: Whisk 4 ounces softened cream cheese, 1 tablespoon whole milk, 1 teaspoon vanilla extract, and 1½ cups (6 ounces) confectioners' sugar in medium bowl until smooth.
Transfer to wire rack and top buns with ½ cup glaze; cool 30 minutes. Using foil overhang, lift buns from pan and top with remaining glaze. Serve.To Make Ahead: After transferring pieces to prepared pan in step 7, buns can be covered with plastic wrap and refrigerated for 24 hours. When ready to bake, let sit at room temperature for 1 hour. Remove plastic wrap and continue with step 8 as directed.