Preheat the Oven: Set your oven to 375°F.
Cook the Vegetables: Heat olive oil in a 10–12-inch oven-safe skillet over medium-high heat. Add the bell pepper, onion, and a pinch of salt. Reduce heat to medium and cook, stirring occasionally, until the vegetables are tender (about 10 minutes). Add the garlic, cumin, turmeric, paprika, and cayenne; cook until fragrant, about 1 minute.
Prepare the Tomato Sauce: Stir in the yellow tomatoes, ½ teaspoon salt, and ¼ teaspoon black pepper. Partially cover the skillet and cook until the tomatoes and peppers are soft, forming a thick sauce (about 15 minutes). If the mixture starts to stick to the skillet before breaking down, add a splash of water. Stir in the goat cheese and dill.
Add the Eggs: Create small wells in the tomato sauce and crack an egg into each. Season the eggs with a pinch of salt and pepper.
Bake the Dish: Transfer the skillet to the oven and bake until the eggs are just set, about 7–10 minutes.
Garnish and Serve: Sprinkle with extra dill, chives, and black pepper. Serve warm with fresh pita bread on the side.