Easy Cinnamon Rolls

For the Dough

• 4 tablespoons unsalted butter
• ½ cup water
• ½ cup milk whole or 2% is fine, avoid skim
• 1 packet (2 ¼ teaspoons) instant or rapid rise yeast
• 3 cups all purpose flour plus more for kneading and rolling
• 3 tablespoons granulated sugar
• 1 teaspoon salt
• 1 large egg
• a few drops of vegetable oil for the bowl

For the Filling

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

For the Icing

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