Cook pasta in a large pot of salted boiling water according to package instructions. Reserve ½ cup pasta water, then drain.
Meanwhile, finely chop onion, and tear pale inner leaves of escarole to yield 4 cups (reserving the rest for another use).
Heat oil in a large straight-sided skillet over medium-high.
Add onion and garlic, season with salt and pepper, and cook, stirring, until onion is translucent, about 3 minutes.
Add tomato paste; cook 1 minute.
Add beans and their liquid, broth, and ¼ cup pasta water (or a bit more, if you prefer your pasta creamier); simmer until slightly reduced, 3 to 4 minutes.
Stir in pasta, cheese, and 3 cups escarole; season to taste.
Drizzle remaining 1 cup escarole with oil; season to taste.
Serve pasta topped with dressed escarole, drizzled with oil and sprinkled with more cheese.
