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Step 1
Adjust oven rack to middle position and heat oven to 200 degrees. When oven reaches 200 degrees, shut off. Line the bottom of a 13- by 9-inch baking pan with foil or parchment paper. Grease foil or parchment paper and sides of the pan. Also, grease a medium bowl to hold the dough when it's completed.
Step 2
Whisk heated 110 degree milk and yeast in liquid measuring cup until yeast dissolves, then whisk in eggs and vanilla extract. In bowl of stand mixer fitted with dough hook, mix flour, cornstarch, sugar, and salt until combined. 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 butter, one piece at a time, until incorporated. I added my butter in 4 second intervals. Continue to mix until dough is smooth and comes away from sides of bowl, about 10 minutes. if after mixing for 10 minutes the dough is still wet and sticky, add up to ¼ cup flour (one tablespoon at a time) until the dough releases from the bowl. 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 turned off oven. Let rise until doubled in size, about 2 hours.
Step 3
Combine brown sugar, cinnamon, and salt in small bowl using a fork or your fingers to break up any large lumps. Turn dough out onto lightly floured surface. Roll dough into 18-inch square, spread with 5 tbsp of softened butter, and sprinkle evenly with filling. Lightly press the filling into the dough. Starting with the edge nearest you, roll dough into tight cylinder, pinch lightly to seal seam, and cut into 8 pieces using either a serrated knife or bench scraper. It's easier to cut the dough in half, then cut each side in half until you have 8 large rolls. For smaller cinnamon buns, cut the dough into 12 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.
Step 4
Heat oven to 350 degrees. Whisk cream cheese, butter, ¼ milk, vanilla, vanila bean and confectioners’ sugar in medium bowl until smooth. If mixture is too thick, add a little more milk, up to ½ half cup. Discard plastic wrap and bake buns until deep golden brown and filling is melted, 35 to 40 minutes. Cool for about 5 minutes then pour over some of the glaze. You may not have to use all of the glaze, I didn't. I stored the rest of the glaze in the freezer for later use. Serve immediately.
Step 5
*Make Ahead: After transferring pieces to prepared pan in step 3, 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 4 as directed.
Step 6
*Reheat any leftover rolls in the microwave for 10 to 20 seconds.