Heat oven to 375 degrees.
Heat oil in a large skillet over medium-low heat. Add onion and bell pepper. Cook gently until very soft, about 20 minutes. Add garlic and cook until tender, 1 to 2 minutes; stir in cumin, paprika and cayenne, and cook 1 minute. Pour in tomatoes and season with 3/4 teaspoon salt and 1/4 teaspoon pepper; simmer until tomatoes have thickened, about 10 minutes. Stir in crumbled feta.
Gently crack eggs into skillet over tomatoes. Season with salt and pepper. Transfer skillet to oven and bake until eggs are just set, 7 to 10 minutes. Sprinkle with chives and serve with hot sauce.