A Parmesan rind is the powerhouse ingredient behind this fast, flavorful version of the classic soup.
In a medium saucepan, heat oil over medium. Add sausage; cook, turning occasionally, until browned, 8 to 10 minutes. Transfer to a plate. Add onion, fennel, and a pinch of salt to pot. Cook, stirring, until softened, 10 minutes (if browning too quickly, add a splash of water). Add broth, 3 cups water, and rind. Season with salt and pepper. Bring to a boil, then reduce heat and simmer 5 minutes.
Meanwhile, toast pastina in a dry skillet over medium-high heat, stirring often, until golden, about 4 minutes. Add to simmering broth. Slice sausage; add to saucepan with accumulated juices. Cook, stirring, until pastina is al dente and sausage is cooked through, 6 to 8 minutes. Drizzle escarole with vinegar; season with salt and pepper and divide evenly among bowls. Ladle soup over it; top with shaved cheese, fennel fronds, and pepper.