Peel the carrot if desired, then finely grate it using a box grater or food processor. Set aside.
Wash the apple thoroughly. Core it and dice into small cubes, leaving the peel on for added fiber.
In a small saucepan, add rolled oats, milk or water, grated carrot, diced apple, cinnamon, nutmeg (if using), and a pinch of salt.
Place the saucepan over medium heat and bring the mixture to a gentle simmer, stirring occasionally to prevent sticking.
Once simmering, reduce the heat to medium-low and cook for 5–7 minutes, stirring frequently.
Continue cooking until the oats are tender, the apples are soft, and the carrots are fully integrated into the mixture.
Remove from heat and stir in vanilla extract and sweetener if using. Taste and adjust seasoning as needed.
Transfer the oatmeal to a serving bowl.
Top with dried fruit, nuts, seeds, or an extra sprinkle of cinnamon if desired.
Serve warm and enjoy immediately.