Preheat broiler. Cut baguette into 1-inch thick slices and cut each slice cut into quarters. In a bowl, toss bread with 1 tbsp of the oil. Transfer to baking sheet and broil under preheated broiler, watching closely and turning several times, until evenly browned. Remove from oven. Sprinkle with paprika and set aside.
In a large saucepan, heat remaining oil over low heat. Add chorizo and cook, stirring, for 3 minutes. Add garlic and cook, stirring, until fragrant, about 1 minute. (Do not brown.) Stir in stock and reserved bread. Reduce heat and simmer until bread is very swollen, about 6 minutes. Season to taste with salt and black pepper.
One at a time, break eggs into a ladle or a cup and slide gently into the soup. Cover and simmer until the whites are firm but the yolks are still soft, about 3 minutes.
Carefully ladle into warm serving bowls, including an egg in each serving. Sprinkle with parsley. Serve immediately.