Preheat the oven to 400°F (200°C).
Add feta, Greek yogurt, 1 tablespoon olive oil, lemon zest, lemon juice, roughly chopped garlic, and black pepper to a small food processor. Blend until smooth and creamy. Set aside.
Add halved cherry tomatoes to a 9-inch oven-safe skillet or small baking dish. Toss with 1 tablespoon olive oil, minced garlic, oregano, optional red pepper flakes, and black pepper.
Roast the tomatoes for 12 to 15 minutes, until softened, wrinkled, and juicy.
Remove the dish from the oven. Stir in the baby spinach until it begins to wilt. Spoon the creamy feta into the center of the dish.
Use the back of a spoon to make four shallow wells in the feta and tomato mixture. Crack one egg into each well.
Return the dish to the oven and bake for 8 to 12 minutes, until the egg whites are set and the yolks are cooked to your preferred doneness. For fully cooked egg dishes, bake until the center reaches 160°F (71°C) and the yolks are firm.
Remove from the oven and let rest for 2 minutes. Top with fresh herbs, extra feta, red pepper flakes, or lemon zest if desired.
Serve immediately with warm pita bread or toasted sourdough and lemon wedges.