Special equipment: a 2-quart baking dish or an 8-inch square baking pan
For the oatmeal: Preheat the oven to 350 degrees F. Grease a 2-quart baking dish or an 8-inch square baking pan with the butter.
Stir together the oats, sugar and salt in a large bowl. Whisk together the almond milk, vanilla and egg in a medium bowl. Pour the milk mixture into the oat mixture and stir to combine.
For the topping: In a medium bowl, stir together the walnuts, oats, sugar, butter, flour, pumpkin pie spice and salt.
Pour the oatmeal into the prepared baking dish. Scoop heaping tablespoons of the pumpkin puree directly into the oatmeal, and sprinkle the topping over the dish. The mixture will be very wet at this point, but the oats will soak up the liquid. Bake until lightly browned and just set, about 50 minutes.
Cool on a rack for 10 to 15 minutes. Serve warm.
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