Bring three cups of water to a boil in a large saucepan. Stir in the oats and salt, then cover the pan and remove it from the heat. Let the grains stand for at least 7 hours or up to 12 hours—this long soak hydrates the oats so they soften without hours of simmering.

Heat the oil in a 12-inch skillet over medium-high heat until the oil should shimmer but not smoke. Add the mushrooms and onion and cook until the mushrooms have browned and the onion is softened, about 5 minutes.

Stir in the garlic and cook until fragrant. Add the soaked oat mixture and the remaining cup of water to the skillet.

Simmer the mixture over medium-high heat, stirring occasionally, until the oatmeal is thickened and the grains are tender, 4 to 6 minutes.

Stir in the spinach, peas, Parmesan, and parsley. Cook until the spinach is wilted and the cheese has melted into a creamy sauce. Season with salt and pepper to taste and serve immediately while hot.