Heat olive oil in a large, heavy-bottomed skillet over medium-high heat. Add the onion, garlic, bell pepper, and chilies. Sauté for 3 to 5 minutes until the vegetables become tender and begin to caramelize. Stir in the tomato paste, sweet paprika, and smoked paprika, cooking for another minute until fragrant.
Add the diced tomatoes and brown sugar, mixing well. Lower the heat and let it simmer for 15 to 20 minutes. Incorporate the kale into the tomato mixture and stir. Crack the eggs individually into the sauce, spacing them evenly. Reduce the heat to low and cook for about 5 minutes, or until the eggs reach your desired doneness. Garnish with parsley, season with salt and pepper to taste, and serve with crusty bread.