Step 1
Stir 1 garlic clove, finely chopped, ¼ cup extra-virgin olive oil, ¼ cup (loosely packed) finely chopped parsley, and a big pinch of kosher salt in a small bowl to mix. Set garlic combination apart at room temperature till able to serve.
Step 2
Warmth ½ cup extra-virgin olive oil in a big Dutch oven or different heavy pot over medium. Working in batches if wanted, add 8 oz. baguette or country-style bread, halved lengthwise, lower facet down, and prepare dinner till deep golden brown beneath, 5–8 minutes, relying on thickness. Switch bread to a plate, leaving oil behind.
Step 3
Scale back warmth to low. Add 1 medium onion, sliced, and 6 garlic cloves, coarsely chopped, to pot and prepare dinner, stirring usually, till onion is softened and golden brown across the edges, 5–8 minutes. Add 2 Tbsp. rooster or vegetable bouillon paste, 1 Tbsp. smoked paprika, 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, ¼ tsp. crushed crimson pepper flakes, and 5 cups water. Stir to mix, then deliver to a simmer. Tear toasted bread into massive (about 3″) items and add to pot. Enhance warmth to medium-high, cowl, and prepare dinner, adjusting warmth as wanted to take care of a simmer, till bread is swollen and really gentle, 15–18 minutes. Take away from warmth.
Step 4
Utilizing an immersion blender, fastidiously mix soup in pot till very clean. (Alternatively, you’ll be able to mix in batches in a daily blender, transferring to a medium bowl as you go. Return soup to pot earlier than continuing.) Return pot to medium-low warmth and reheat soup, stirring and thinning with extra water if wanted (soup ought to be the consistency of heavy cream). Stir in 1 tsp. sherry vinegar or crimson wine vinegar; season with freshly floor pepper. Style and season with extra salt if wanted. Scale back warmth to low, cowl, and preserve heat till able to serve.
Step 5
Warmth 1 Tbsp. extra-virgin olive oil in a big nonstick skillet over medium. Crack 3 massive eggs into skillet and prepare dinner till whites are simply set, about 4 minutes; switch to a plate and season with salt and pepper. Repeat with remaining 1 Tbsp. extra-virgin olive oil and 3 massive eggs.
Step 6
Ladle soup into bowls and high every with a fried egg and a few reserved garlic combination. Season with extra pepper. Finely grate Parmesan or Manchego cheese over if desired.
