Gingerbread Baked Oats

Name: Gingerbread Baked Oats
Ingredients: 2 cups whole milk plus 1½ tablespoons , divided, plus more as needed; 1 large ripe banana , mashed; 2 large eggs; 3 tablespoons dark brown sugar; 2 tablespoons unsalted butter , melted; 1 tablespoon vanilla extract plus ½ teaspoon , divided; 1½ teaspoons ground cinnamon; 1 teaspoon baking powder; 1 teaspoon ground ginger; ¼ teaspoon ground allspice; ¼ teaspoon salt; ⅛ teaspoon ground cloves; ⅛ teaspoon ground nutmeg; 2½ cups old-fashioned rolled oats; 3 ounces cream cheese , softened; 1 tablespoon confectioners’ sugar , plus more for garnish