Heat oil in a Dutch oven over medium. Add onion and carrots; cook, stirring occasionally, until tender, about 5 minutes. Add garlic, tomato paste, smoked paprika, cumin, salt, black pepper, and red pepper; cook 1 minute. Add kale and lentils; cook, stirring often, until kale begins to soften, about 2 minutes. Add stock and 2 1/2 cups water; increase heat to high. Bring to a boil. Reduce heat to medium, and simmer until lentils are tender, about 30 minutes. Form 5 indentations in soup. Crack eggs, 1 at a time, into a small custard cup. Gently slip 1 egg into each indentation. Cover and cook over medium-low until egg whites are set, about 6 to 8 minutes.