Bring a large pot of salted water to a boil. Add the tortellini and cook until tender, about 4 minutes. Reserve 1 cup cooking water, then drain.
Return the pot to medium heat and add the butter and 1/2 cup of the reserved cooking water. Cook, swirling the pot, until the butter melts and combines with the water. Add the tortellini and arugula and gently toss to coat, adding more cooking water as needed to loosen. Season with salt.
Divide the tortellini among bowls. Season generously with pepper and sprinkle with the parmesan. Top with the prosciutto.