Bring a small pot of water to a gentle simmer for poaching eggs, or heat a non-stick skillet over medium heat for frying.
If poaching: Crack each egg into a small bowl or ramekin. Gently slide the eggs into the simmering water and cook for 3–4 minutes for soft yolks or until desired doneness.
If frying: Lightly grease the skillet with olive oil. Crack eggs directly into the pan and cook sunny-side up or to your preference, about 2–3 minutes per egg.
While eggs cook, warm the pesto in a small saucepan over low heat or microwave for 30 seconds to loosen if too thick.
Once eggs are cooked, transfer them to serving plates. Spoon warm pesto over each egg, sprinkle with red pepper flakes, salt, and pepper.
Garnish with grated Parmesan and fresh basil leaves before serving immediately.
Notes
Serve immediately while eggs are hot and pesto is warm for最佳 flavor.