Heat 2 tbsp. oil in a 12-in. cast-iron skillet over medium-high heat on a camp stove. Sauté onion and fresh chiles, if using, until softened, 7 to 8 minutes. Add canned chiles, if using, garlic, cumin, 1/2 tsp. salt, and the paprika; cook, stirring, until garlic is softened, about 1 minute.
Add tomatoes and sugar; bring to simmering, then reduce heat and cook until flavors are blended and mixture is a little thicker, about 15 minutes. Stir in 1 tbsp. parsley.
With a wooden spoon, make 6 depressions in tomato mixture. Crack 1 egg into each and sprinkle with salt and pepper. Cover skillet tightly with a lid or foil. Cook until eggs are set but yolks are still runny, rotating skillet 180° halfway through cooking, 5 to 9 minutes.
Scatter feta and remaining 3 tbsp. parsley over shakshouka, then drizzle with remaining 2 tbsp. oil. Serve with more oil at the table if you like.