Add oil to a large cast iron skillet over medium-high heat.
When oil is hot, add squash, onion and bell pepper, season with salt and pepper, and sauté, stirring often, until softened, about 5-7 minutes.
Move the squash to one side of the skillet and add the butter to the open side of the skillet to melt. Stir the dill and garlic into the butter, and once the mixture barely starts to bubble, toss the squash mixture into the butter mixture, stirring to coat. Spread squash evenly across the pan and then remove the pan from heat.
Preheat the oven to 350 F. Make four small wells in the squash mixture, and then crack an egg into each well. Season each egg with salt and pepper, and then carefully put the pan in the oven.
Cook until eggs are desired doneness (15-20 minutes for a runny yoke, 20-30 for a harder yoke)
Sprinkle with chopped tomato, feta and extra dill, and serve immediately!