Bring the first measure of water to a boil in a large saucepan over high heat. Remove the pan from the heat and stir in the oats and salt. Cover the pan and let it sit for at least 4 hours or up to 12 hours.

Stir the remaining water into the oats and bring to a boil over medium-high heat. Reduce the heat to medium and cook, stirring occasionally, until the oats are softened but still retain some chew, about 4 to 6 minutes. The mixture should thicken and resemble warm pudding. Remove the pan from the heat and let it rest for 5 minutes.

Heat the oil in a 12-inch nonstick skillet over medium heat until it shimmers. Add the mushrooms, onion, and salt and cook, stirring often, until the vegetables are softened and translucent, about 5 minutes.

Stir in the garlic and cook until fragrant. Add the spinach and peas and cook until the spinach is completely wilted and the peas are bright green, about 2 minutes.

Season the vegetable mixture with pepper to taste, then stir the vegetables, Parmesan, and parsley into the cooked oats. Serve immediately while hot and creamy.