Heat the oil in a large saucepan over medium-high heat until very hot but not smoking. Add the garlic and fry until golden brown, about 1 minute. Using a slotted spoon, transfer the garlic to a plate. Add the bread, cut side down, and cook, turning once, until golden brown, about 3 minutes. Transfer to the plate with the garlic.

Return the garlic to the saucepan. Add the broth and paprika, bring to a boil, and cook to blend the flavors, about 5 minutes. Season with salt and pepper. Reduce the heat to medium-low so the broth is simmering. Crack an egg into a small bowl; then slip the egg into the simmering broth. Repeat with the remaining eggs. Simmer until the whites are set (you are basically poaching the eggs in the broth), about 4 minutes.

Ladle the soup into 4 soup bowls. Using a slotted spoon, transfer a poached egg to each bowl. Top with a fried bread slice. Sprinkle with parsley and serve hot.