Heat 2 tbsp olive oil in a medium saucepan over medium-high heat. Add the sliced mushrooms and cook, stirring occasionally, about 6 minutes until golden. Stir in the minced garlic and cook 30 seconds. Transfer mushrooms to a plate.

Melt 1 tbsp butter in the same pan over medium heat. Add 1 cup steel-cut oats and toast, stirring, for about 2 minutes until nutty and slightly darker.

Pour in 2 cups broth, 1 cup milk, add ½ tsp salt and the thyme. Bring to a boil, then reduce heat and simmer, stirring often, for 20–25 minutes until tender and creamy.

Remove from heat, fold in ¼ cup Parmesan and most of the mushrooms. Season with salt and pepper. Fold in spinach now if using.

For the egg, heat a nonstick skillet with a drizzle of oil over medium heat. Fry the eggs 2–3 minutes until whites are set. Top each bowl with the remaining mushrooms, an egg, and extra Parmesan. Serve hot.