Begin by preheating your oven to 400°F (200°C).
Take a suitable baking dish and position the block of feta cheese in the middle. Scatter the halved cherry tomatoes around it.
Generously drizzle the extra virgin olive oil over both the feta and tomatoes. Season with dried oregano, sea salt, and freshly ground black pepper.
Place the dish in the oven and bake for about 20 minutes, or until the feta becomes creamy and the tomatoes start to char.
Carefully take the dish out of the oven and gently crack the eggs on top of the warm feta and tomatoes.
Place the dish back in the oven and bake for an additional 10-12 minutes, watching closely until the egg whites are firm but the yolks remain slightly runny.
Once done, allow it to cool for a minute before garnishing with fresh basil or parsley if you like.