For the Dough

• 4 tablespoons butter unsalted
• ½ cup water
• ½ cup milk whole or 2% is fine, avoid skim
• 1 packet instant yeast or rapid rise yeast
• 3 cups all-purpose flour plus more for kneading and rolling
• 3 tablespoons granulated sugar
• 1 teaspoon salt
• 1 egg large
• vegetable oil a few drops, for the bowl

For the Filling

• ¼ cup brown sugar
• ¼ cup granulated sugar
• 1 tablespoon cinnamon
• ¼ teaspoon salt
• 4 tablespoons butter plus one extra tablespoon for the pie plate, melted, unsalted

For the Icing

• 8 oz cream cheese softened to room temperature
• 2 tablespoons butter softened to room temperature, unsalted
• 1 cup powdered sugar
• 1 teaspoon vanilla extract
• pinch salt optional