Spread hazelnuts onto a baking tray. Toast hazelnuts in oven until light golden brown and fragrant, about 5 to 7 minutes. Allow to cool completely. Coarsely chop the cooled hazelnuts and set aside.
In a 10 or 12-inch saute pan with high sides, bring 2 quarts of salted water to a boil. Add the vegetable oil to prevent the ravioli from sticking to one another. Add ravioli and cook for 4 minutes or until they float to the top. Using a spider strainer, carefully remove ravioli to a large platter and tent with foil to keep warm.
In a small saute pan, melt the butter. When butter is sizzling and starts to brown, tear sage leaves into the pan and fry for about 20 seconds. Remove from heat and stir in nutmeg. Pour butter sauce over ravioli and sprinkle with toasted hazelnuts. Grate amaretti cookies over the dish and serve immediately.