4 ounces high-quality baguette
1/2 cup olive oil, divided
1 garlic head (about 12 cloves), peeled and finely chopped
1 heaping tablespoon Pimentón de la Vera (smoked Spanish paprika)
8 cups homemade or low-sodium chicken broth
2 teaspoons kosher salt, plus more to taste
2 tablespoons sherry vinegar
3 large eggs, beaten
Preheat oven to 450°F. Place baguette on a baking sheet, and toast in preheated oven until very browned and almost burnt, 20 to 25 minutes. Remove from oven, and let cool. Break or slice bread into 2-inch pieces.
Heat 7 tablespoons oil in a large pot over medium-high. Add bread pieces, and reduce heat to medium. Cook, turning often to allow bread to toast and soak up oil, until golden brown, about 2 minutes. Remove bread, and set aside. Wipe pot clean.
Add garlic and remaining 1 tablespoon oil to pot. Cook over medium-high, stirring constantly, until garlic is golden brown, 30 seconds to 1 minute. Stir in paprika. Add broth and salt; bring to a boil.
Add bread to pot. Reduce heat to medium-low, and maintain a simmer. Add vinegar. Cook, stirring occasionally to break up bread, until flavors meld, about 25 minutes. Taste and add more salt, if needed.
When ready to serve, bring soup to a simmer over medium-high. Stirring constantly, slowly pour beaten eggs into hot soup. If any large pieces of bread remain, cut with kitchen scissors, or break apart with a spoon. Serve hot.
Notes: Soup can be prepared through step 4 up to 2 days in advance. Bring to a simmer, and add beaten eggs just before serving.