In a food processor, combine lamb, cheeses, hazelnuts, basil, shallots, garlic, egg yolks, salt and pepper. Blend until a doughy consistency is reached. Portion out 24 balls. Cut pasta into 48 portions. Brush egg white onto edges of each pasta sheet, place lamb mixture in center, cover with a second pasta sheet, and crimp with fork to create ravioli shape. Bring a 6-quart pot filled with 4 quarts of water to a boil. Add 2 teaspoons salt. Reduce to a gentle boil and add ravioli in batches. Cook 2 to 3 minutes. Remove and keep warm. Finish with a drizzle of Apple Cider-Ginger Reduction.
For Apple Cider-Ginger Reduction: In a saucepan, combine cider, ginger and salt. Simmer over low heat. Reduce sauce to a syrup consistency.