Bring 12" sauté pan of water to a boil and generously season with salt. Prepare a rimmed sheet pan with parchment paper. Cook pasta according to package directions until al dente. Remove ravioli using a slotted spoon and place in a single layer on the sheet pan, then discard water.
Place the pan over medium heat. Add oil, butter, and garlic; sauté until butter begins to bubble, about 1 minute. Add red pepper flakes, salt, and pepper; stir with a rubber spatula. Add half the ravioli and stir gently until well coated; immediately add balance of ravioli and repeat. Flip the ravioli gently as needed to prevent them from sticking. Cook ravioli until golden brown, about 5 minutes.
Toss in spinach gently, then garnish with parsley and Parmesan. Serve immediately.