In a medium saucepan, heat olive oil over medium heat. Add the diced onion and sauté until translucent, approximately 4 minutes.
Add the minced garlic and sauté for 60 seconds until fragrant.
Incorporate the rolled oats into the saucepan and toast for 2 minutes, stirring frequently to prevent burning.
Add the broth and salt to the saucepan. Bring the liquid to a simmer.
Reduce the heat to low, cover the pan, and cook for 10 to 12 minutes until the liquid is fully absorbed and the oats reach a creamy consistency.
While the oats are simmering, prepare the eggs using a poaching or frying method until the whites are set but the yolks remain liquid.
Remove the oats from the heat and fold in the Parmesan cheese and black pepper.
Portion the oatmeal into two bowls, top each with a prepared egg, and garnish with minced chives.