Preheat the oven to 350°F. Lightly grease an 8×11-inch baking dish.
Add the pumpkin puree, eggs, maple syrup, whole milk, and vanilla extract directly to the prepared baking dish. Whisk until smooth and well combined.
Add the old-fashioned oats, almond flour, ground flaxseed, baking powder, pumpkin pie spice, cinnamon, and salt. Stir until everything is evenly combined.
Spread the mixture evenly in the baking dish. Bake for 25–28 minutes, or until the center is set and the oats are lightly golden around the edges.
Remove from the oven and allow the baked oats to cool for about 15 minutes.
Make the maple cream cheese icing. While the oats cool, beat the softened cream cheese and maple syrup until smooth. Add the sifted powdered sugar and beat again until creamy and well combined.
Drizzle the maple cream cheese icing over the slightly cooled baked oats. Add whipped cream, if desired, and serve warm.