Heat 1 tablespoon oil in a large saucepan over medium heat. Add shallot and cook, stirring occasionally, until softened, 1 to 2 minutes. Add oats and stir for 1 minute. Add 4 cups water and 1/4 teaspoon each salt and pepper. Bring to a boil, then reduce heat to a simmer. Cook, stirring often, until creamy, 10 to 12 minutes.