In a large saucepan, heat the chicken stock until bubbles appear around the edge. Drop the bread into a food processor and pulse until coarse crumbs form. Add the cheese and pulse until finely chopped. Transfer the mixture to a large saucepan and gradually whisk in 8 cups of the stock. Cook over moderate heat, stirring constantly with a wooden spoon, just until the soup begins to simmer. Keep warm over very low heat.
Gradually whisk the remaining 2 cups of chicken stock into the egg yolks, then whisk this mixture into the soup. Using an immersion blender, blend the soup until smooth and frothy. Alternatively, carefully puree the soup in batches in a blender. Ladle the soup into warmed soup plates and garnish with a drizzle of olive oil and a sprinkling of pepper.