Heat the oil in a large skillet over medium heat then add the shallots and stir for 1-2 minutes. Next, add the oats and water, stir, and bring to a boil, then reduce heat to a simmer and simmer oats for 15-20 minutes, stirring occasionally until oats are cooked.
While oats are cooking, heat oil in a separate skillet, then add the brussels sprouts and sweet potato, sprinkle them with salt and pepper and cook over medium-high heat, stirring occasionally until they're cooked. Note: you may need to add more oil so that they cook faster.
Once the sprouts and potatoes are cooked, turn the heat down to low and use a spatula to create a hole in the center of the skillet; then, crack an egg in the center. If you're cooking two eggs, create two holes. Fry the egg(s) until it's cooked all the way through.
Once the oats are cooked, stir in the cheese until it's melted.
To assemble: pour oats into a bowl then top them with the brussels sprouts, potatoes, egg, and last but certainly not least, the Cholula!