Cut the stale crusty bread into 1-inch cubes and spread on a baking sheet. Toast in a 350°F oven for about 8-10 minutes, stirring halfway through, until the cubes are golden and slightly crispy on the outside but still have some give inside. This prevents them from dissolving into mush when the stock is added. While the bread toasts, thinly slice the garlic cloves into uniform slivers—uniformity ensures even cooking and prevents some pieces from burning while others remain raw. Whisk the eggs in a small bowl and set aside.
Heat the olive oil in a large pot over medium heat. Once shimmering, add the sliced garlic and cook gently for 2-3 minutes, stirring frequently, until the garlic turns golden and becomes fragrant—be careful not to let it brown or turn dark, as this will make the soup bitter. Immediately stir in the smoked paprika, mixing constantly for about 30 seconds to bloom the spice and release its deep, smoky flavor into the oil. This is where the soul of the soup develops.
Add the toasted bread cubes from Step 1 to the garlic-paprika oil and stir constantly for about 2-3 minutes, coating the bread well and allowing it to absorb the flavored oil. Pour in the chicken stock, stirring gently to distribute the bread throughout. Bring the soup to a simmer over medium-high heat, then reduce to medium. I like to let it simmer for a couple of minutes before adding the eggs—this allows the bread to begin softening and the flavors to meld together.
Once the soup is gently simmering, use a fork or whisk to stir the soup in slow, deliberate circles. While stirring continuously, slowly drizzle the whisked eggs from Step 1 into the moving soup in a thin stream—this creates silky ribbons of cooked egg throughout rather than scrambled pieces. The constant motion and gentle heat are crucial here; if you pour too quickly or stop stirring, the eggs will clump. Continue stirring for about 1 minute after all the egg is added to ensure it's evenly incorporated and cooked through.
Taste the soup and season generously with sea salt and freshly ground black pepper. Stir in the sherry vinegar if using—it adds a subtle brightness that complements the smoky paprika and sweet garlic perfectly. Adjust seasonings as needed, keeping in mind that you want each spoonful to be deeply flavorful.
Ladle the hot soup into bowls while it's still steaming. The bread should be mostly softened but still have some texture, the egg should be visible as delicate ribbons throughout, and the broth should have a beautiful golden color from the garlic and paprika. Serve immediately with extra crusty bread on the side if desired.