In a small saucepan over low heat, warm 1 cup whole milk and 6 tablespoons unsalted butter until the butter melts and the mixture reaches about 105°F (40°C). Remove from heat and let it cool slightly.
In a large bowl, whisk together 4 cups bread flour, 1/3 cup granulated sugar, 2 1/4 teaspoons active dry yeast, and a pinch of salt.
Make a well in the center, then add the warm milk mixture and 1 beaten large egg. Stir with a wooden spoon until the dough just comes together.
Turn the dough out onto a lightly floured surface and knead for 8 to 10 minutes, until smooth and elastic.
Place the dough in a lightly oiled bowl, cover with plastic wrap or a clean kitchen towel, and let it rise in a warm spot for 1 to 1 1/2 hours, until doubled in size.
Meanwhile, in a medium bowl, beat 7 tablespoons softened unsalted butter with 2/3 cup packed light brown sugar and 2 tablespoons ground cinnamon until smooth and spreadable.
Punch down the dough, then roll it out on a lightly floured surface into a 16×12-inch rectangle. Spread the cinnamon filling evenly over the dough, leaving a 1/2-inch border around the edges.
Starting from one of the long sides, roll the dough into a tight log. Using a sharp knife or kitchen scissors, cut the log into 12 equal pieces, about 1 1/2 inches thick.
Arrange the rolls on a baking sheet lined with parchment paper, leaving a little space between them. Cover loosely and let them rise for 30 to 45 minutes, until puffy.
Meanwhile, preheat your oven to 350°F (175°C).
Bake the rolls for 20 to 25 minutes, or until golden brown.
In a small bowl, whisk together 1 1/4 cups powdered sugar, 2 1/2 tablespoons milk (or cream cheese for a thicker glaze), and 1/2 teaspoon vanilla extract until smooth.
Drizzle the glaze over the warm rolls and serve.