Put the oats and 3½ cups water into a heavy medium saucepan along with the salt — use 4 cups water if you prefer a looser porridge texture. Bring to a boil, stir the oats, then lower heat to a slow simmer.
Cook until most of the water is absorbed (stirring occasionally) and the oats begin to get creamy, 25-30 minutes (they won't be totally soft at this point, but pleasantly chewy).
Remove from the heat and stir in the olive oil, cheese and about 1/2 teaspoon pepper.
To make the poached eggs:
When the oats are almost ready, bring a small skillet of water to a boil with the vinegar - a non-stick pan makes for easier cleaning. Crack the eggs into the water and adjust the heat down from a boil to a simmer. Cook the eggs until they are done to your liking, about 5 minutes for softly-set yolks.
Serve the oats with a poached egg on top. Top with more cheese to taste. If you have a hunk of cheese, use a swivel vegetable peeler to shave additional cheese over the top.
Serving ideas: Top with a fried egg instead, and add a spoonful of your favorite pesto. So good!
To make ahead: Cool and refrigerate up to 3 days. Stir in a little water and reheat gently on the stovetop until hot.