In a medium saucepan, bring the water or vegetable broth to a boil. Add the oats and salt, reducing the heat to a simmer. Cook, stirring occasionally, until the oats are soft and have absorbed the liquid, about 5-7 minutes.
While the oatmeal cooks, heat 1 tablespoon of olive oil in a skillet over medium heat. Add the spinach and sauté until just wilted, about 2-3 minutes. Season with a little salt to taste.
Bring a small pot of water to a gentle simmer and add a teaspoon of vinegar. Crack an egg into a small bowl and gently slide it into the simmering water. Repeat with the second egg. Poach the eggs for about 3-4 minutes, or until the whites are set but the yolks are still runny. Remove the eggs with a slotted spoon and set them on a paper towel to drain.
Divide the cooked oatmeal between two bowls. Top each with the sautéed spinach and a poached egg. Season with paprika, freshly ground black pepper, and an extra sprinkle of salt if needed.
Drizzle each serving with a bit more olive oil for richness and serve immediately