Preheat the oven to 400°F.
If using individual ramekins, divide tomatoes, bell pepper, red onion, garlic, and feta cheese evenly among 4 oven-safe dishes. Drizzle 1 tablespoon olive oil over each.
If using one large baking dish (8x8 or 9x11), combine tomatoes, bell pepper, red onion, and garlic in the dish, place feta in the center, and drizzle olive oil over all.
In a small bowl, mix dried oregano, sea salt, dried thyme, black pepper, and red pepper flakes. Sprinkle the spice mixture evenly over the feta and vegetables.
Place ramekins on a baking sheet or place the baking dish directly on the oven rack. Bake for 25 minutes.
Remove from oven and stir to combine feta with the vegetables. Add chopped spinach and stir until evenly mixed.
Create wells in the mixture and crack one egg into each well.
Return the dishes to the oven and bake for an additional 10 minutes until eggs are set.
Top with optional chopped fresh basil or chives and serve with crusty bread, toast, or pita for dipping.