Add water, oats, pumpkin puree, pumpkin pie spice, cinnamon, and salt to the inner pot of an electric pressure cooker and stir to combine. It's fine if the pumpkin doesn't totally incorporate, it'll cook into the oats while pressure cooking.
Lock lid in place and turn steam vent handle to Sealing. Cook on High Pressure for 12 minutes for firmer steel cut oats, or 14 minutes for softer oats.
Turn steam vent handle to Venting to quick-release pressure. Remove lid and stir butter and brown sugar into oatmeal.