To prepare rolls, combine milk, 1 tablespoon granulated sugar, and yeast in the bowl of a stand mixer, stirring with a whisk. Let stand 5 minutes. Stir in 2 tablespoons butter, 1/4 cup granulated sugar, and egg. Weigh or lightly spoon flour into dry measuring cups; level with a knife. Add flour and salt to yeast mixture. Mix on low speed with dough hook just until combined; mix on medium-low speed 6 minutes. Scrape dough into a large bowl coated with cooking spray (dough will be very soft and sticky). Coat top of dough with cooking spray; cover and let rise in a warm place (85°F), free from drafts, 45 minutes or until doubled in size. (Press two fingers into dough; if indentation remains, dough has risen enough.)
Punch dough down; turn out onto a well-floured work surface. Roll dough into a 15 x 11–inch rectangle. Brush dough with 2 tablespoons butter. Combine brown sugar and cinnamon; sprinkle mixture evenly over dough, spreading all the way to edges. Gently roll up dough jelly-roll style, starting with a long end. Cut dough into 15 (1-inch) slices using a sharp serrated knife. Arrange slices in a 13 x 9–inch glass or ceramic baking dish coated with cooking spray. Cover and let rise 40 minutes.
Preheat oven to 350°F.
Uncover dough. Bake at 350°F for 22 to 25 minutes or until lightly browned. Cool slightly.
To prepare glaze, combine powdered sugar, syrup, 1 tablespoon melted butter, and 1/4 teaspoon salt, stirring until smooth. Spread glaze evenly over warm rolls. Serve warm.
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