In a medium saucepan over medium-low, combine the scallion whites, garlic and 3 tablespoons of the oil. Cook, stirring occasionally, until beginning to color, 8 to 10 minutes.
Add both paprikas and cook, stirring, until fragrant and darkened, 30 seconds.
Add 1 cup of the bread cubes and stir well. Whisk in the water and bouillon, increase heat to medium-high and bring to a simmer.
Reduce heat to medium-low and simmer, whisking occasionally to break up bread, for 15 minutes. Whisk vigorously to ensure bread is thoroughly broken up.
Meanwhile, in a 12-inch skillet over medium, combine the remaining 3 tablespoons oil, the remaining 3 cups bread, the scallion greens, and ½ teaspoon each salt and pepper.
Cook, stirring occasionally, until browned and crisp, 8 to 10 minutes.
In a medium bowl, whisk the egg yolks. Slowly whisk in 1 cup of the hot broth. Remove the soup from the heat. Off heat, vigorously whisk the egg yolks into the soup, then whisk in the vinegar, if using.
Taste and season with salt and pepper. To serve, fill individual bowls with the crouton mixture, then ladle the soup over them. Drizzle with additional oil, if desired.
