Bring a pot of generously salted water to a boil. Cook pasta according to package instructions.
Meanwhile, in a large frying pan over medium-high heat, heat 1 tbsp. oil. Add garlic and red pepper flakes. Cook 15 seconds, then add escarole in batches, tossing with tongs until it wilts and shrinks in the pan, about 6 minutes. Stir in olives and capers; set aside.
Drain pasta, reserving 3/4 cup pasta-cooking water. Set frying pan of escarole over low heat, add pasta and 1/4 cup cooking water, and toss to combine. Stir in remaining 1 tbsp. oil, the butter, and cheeses. Stir to combine, adding more cooking water as necessary. Serve with more parmesan.