Yukon Gold Cinnamon Rolls

Ingredients

• 1 pound yukon gold potatoes, peeled, cut into 2-inch pieces
• 1 tablespoon coarse kosher salt
• 1/2 cup (1 stick) unsalted butter
• 3 large eggs
• 4 1/2 cups (or more) unbleached all purpose flour
• 1/2 cup warm water (105°f to 115°f)
• 3 1/4-ounce envelopes active dry yeast (scant 2 tablespoons)
• 2 tablespoons sugar
• 1 1/3 cups (packed) golden brown sugar
• 2 1/2 tablespoons ground cinnamon
• 3 tablespoons unbleached all purpose flour
• 9 tablespoons (1 stick plus 1 tablespoon) unsalted butter, room temperature
• 2 cups powdered sugar
• 1/4 cup (1/2 stick) unsalted butter, melted
• 2 tablespoons (or more) whole milk
• 1 teaspoon vanilla extract
• 1/8 teaspoon coarse kosher salt