Heat a large saucepot over high heat. Add sausage and cook, stirring occasionally, until brown, 5 minutes. Add garlic; cook 30 seconds. Add spinach and broth. Fill one empty can of broth with water; add to pot. Cover and bring mixture to a boil. Add capellini, cover and boil 2 minutes more.
Meanwhile, heat broiler. Broil bread slices on cookie sheet about 1 minute per side, until toasted. Drizzle each slice with 1 teaspoons oil; sprinkle each with 1/2 teaspoons Parmesan cheese.
Divide soup among 4 large soup bowls and top each serving with prepared toasts.