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- 2 Italian eggplants, sliced in half and cut into 1/2-inch disks
- 1/2 cup extra-virgin olive oil
- Kosher salt and freshly ground black pepper
- 1 medium summer squash, sliced in half and cut into 1/4-inch disks
- 1 medium zucchini, sliced in half and cut into 1/4-inch disks
- 1 medium onion, cut in half and cut into 1/4-inch slices
- 2 medium cloves garlic, thinly sliced
- 1 pint cherry tomatoes, split in half
- 4 eggs
- 2 tablespoons slived chives
- Hot sauce or chili paste for serving
To Cook Eggplant in the Microwave: Season eggplant slices lightly on both sides with salt. Place double layer of paper towels or clean kitchen towel on large plate and lay single layer of eggplant slices on top. Top with 2 more layers paper towels or clean kitchen towel. Top with second large plate and place another layer of paper towels and eggplant on top. Top with third large plate. Microwave on high power until eggplant is easily compressed, about 3 minutes (be careful, plates will be hot). Press eggplant slices firmly between paper towels until compressed. Set aside on a large plate. Repeat microwaving and pressing steps until all eggplant slices are compressed. Continue with step 3. Adjust oven rack to upper-middle position and preheat oven to 400°F.
To Cook Eggpant in Oven: Adjust oven rack to center position and preheat oven to 375°F. Line a rimmed baking sheet with a double layer of paper towels. Spread eggplant slices over towels in a single layer and top with a second layer of paper towels. Top with a second rimmed baking sheet. Bake until eggplant slices are easily compressed, about 30 minutes. Remove from oven and press down on top tray to compress slices. Let cool, then transfer eggplant to a large plate and continue with step 3. Adjust oven rack to upper-middle position and increase heat to 400°F.
Heat 1/4 cup of olive oil in a large non-stick or cast iron skillet over high heat until shimmering. Add eggplant, season to taste with salt and pepper, and cook, stirring and tossing occasionally, until well browned, about 3 minutes. Return to large plate.
Add additional 2 tablespoons of oil to skillet and heat until shimmering. Add squash and zucchini slices, season to taste with salt and pepper, and cook, tossing occasionally, until well browned, about 5 minutes.
Add remaining 2 tablespoons oil to skillet and heat until shimmering. Add onions, season to taste with salt and pepper, and cook, stirring, until onions are softened and just beginning to brown, about 5 minutes. Add garlic and cook, stirring, until fragrant, about 30 seconds. Add tomatoes and cook, stirring, until they soften, about 5 minutes. Return eggplant, zucchini, and squash to skillet.
To complete, divide mixture between four individual oven-safe serving dishes. Create a well in the center of each one and break an egg into it. Bake until egg is barely set but yolk is still soft, about 6 minutes. Alternatively, leave mixture in large skillet, create four wells, break an egg into each, and bake until eggs are barely set but yolks are still soft, about 6 minutes. Season eggs with salt and pepper and sprinkle with chives. Serve immediately with hot sauce or chili paste.