Bring a large pot of salted water to a boil. Cook the ravioli according to the package directions to al dente. Remove the ravioli from the water to a plate or small baking sheet using a slotted spoon, arranging in a single layer.
Add the butter to a large skillet and cook over medium-low heat until the butter melts. Add the garlic, sage, and hazelnuts and cook, stirring frequently, about 2-3 minutes, or until the milk solids from the butter begin to brown and smell nutty.
Remove the garlic from the skillet and reserve for another use. Remove the sage leaves to a plate. (The sage leaves will become crispy as they cool.)
Return the cooked ravioli to the browned butter sauce in the skillet. Add about ¼ cup of pasta water, and season the sauce with kosher salt and freshly ground black pepper to taste. Gently toss the ravioli in the sauce until it's coated. Return the crispy sage leaves to the pan.
To serve, divide the ravioli between plates and sprinkle with Parmesan cheese.