Preheat oven to 350°F. Coat an 8-inch square (2-quart) baking dish with cooking spray.
Combine 1 egg, 2 tablespoons melted butter, 1¼ cups milk, 3½ tablespoons sugar and 1 teaspoon vanilla in a medium bowl; whisk well.
Stir in 2 cups oats, 1 teaspoon baking powder and ½ teaspoon salt until combined.
Fold in 1 cup chopped cranberries.
Transfer the mixture to the prepared baking dish and let stand, uncovered, at room temperature until slightly thickened, about 15 minutes.
Meanwhile, beat 4 ounces softened cream cheese and the remaining 1½ teaspoons milk, 1½ teaspoons sugar and 1 teaspoon vanilla in a medium bowl with an electric mixer on medium-high speed until smooth and creamy, about 1 minute.
Dollop the cream cheese mixture evenly over the oat mixture.
Use a butter knife, offset spatula or wooden pick to swirl the mixture and create a marbled design.
Bake until the oats are lightly browned and set, 30 to 35 minutes.
Let cool on a wire rack for about 15 minutes before serving. Serve warm or at room temperature.
