Yield: 4 to 6 servings.
In a heavy 4-qt. saucepan over medium heat, heat oil. Add sausage and onion; cook and stir until sausage is lightly browned on all sides and onion is golden, about 5 minutes. Add broth, beans, and Parmigiano-Reggiano rind, if using. Bring to a boil; cook until sausage is cooked thro ugh and cheese rind is tender, 10 to 12 minutes.
Meanwhile, pull a vegetable peeler or cheese slicer across Parmigiano-Reggiano to make thin shavings; crumble remaining cheese and set aside. Remove sausage and cheese rind to cutting board. Slice sausage crosswise; cut rind into small cubes; return to soup along with escarole. Return to a boil. Divide soup among soup bowls. Place one toast slice in center of each serving. Arrange Parmigiano-Reggiano shavings on crostini; sprinkle crumbled cheese on soup.