Preheat oven to 450 degrees. In a large bowl, toss the bread chunks with 2 Tbsp. olive oil and salt and pepper to taste. Grease a 9 x 13 inch baking dish and spread the bread into it in an even layer. Set aside.
In the same large bowl, whisk together 1 1/2 Tbsp. olive oil, minced garlic, oregano, tomato paste, sugar, salt, and pepper. Add cherry tomatoes and stir to coat. Spread evenly on a baking sheet lined with parchment paper, pouring any additional olive oil mixture over tomatoes.
Place both the dish of croutons and the baking sheet of tomatoes in the oven. Bake the croutons for 10 minutes and the tomatoes for 20 minutes.
Once both tomatoes and croutons have baked, pour tomatoes over the croutons and gently stir together, adding an additional 1 Tbsp. olive oil. Using a large spoon, make six shallow indentations in the mixture. Crack one egg into each indentation. Season with salt and pepper. Return the baking dish to the oven for another 12 minutes or until eggs are just set.
Let cool for about 5 minutes, then sprinkle crumbled feta over the top and serve.