Select the Sauté setting on the Instant Pot, add the oil, garlic, and ginger, and heat for 2 minutes, until bubbling. Add the mushrooms and sauté for 1 minute, until they begin to wilt and the ginger and garlic begin to brown on the bottom of the pot. Stir in the water and peas, using a wooden spoon to nudge loose any browned bits from the bottom of the pot. Cover with the glass lid and let come up to a simmer (this will take about 8 minutes).
Remove the lid and press the Cancel button to turn off the pot.
Put the miso paste in a small bowl. Ladle 1/4 cup of the liquid from the pot into the bowl, then mash the miso against the side of the bowl and stir until it is fully dissolved. Add the miso mixture and the green onions to the pot and stir to combine.