1. Preheat the oven to 350 degrees F.
2. In a medium cast-iron cocotte, heat the oil over medium heat. Add the garlic and paprika and cook, stirring, for 30 seconds. Add the kale in 2 or 3 batches, allowing it to wilt slightly between batches so it all fits in the pot. Add a good pinch of salt and cook, stirring often, until the kale is softened, 7 to 9 minutes.
3. Stir in the stock and cook until slightly reduced, about 5 minutes more. Add the cheese, a few turns of black pepper, a pinch of red pepper flakes and the lemon juice. Taste and adjust the seasoning as desired.
4. Distribute the kale mixture among 6 mini cast-iron cocottes and create a well in the center of each. Crack an egg into each well. Bake, uncovered, until the whites are cooked but the yolks are still runny; check for doneness at 12 minutes.
5. Top each cocotte with a drizzle of yogurt and a sprinkle of za'atar, parsley, salt and pepper. Serve immediately with crusty bread.
6. Special equipment: a medium cast-iron cocotte; 6 mini cast-iron cocottes