01 - Mound flour on a clean work surface and create a well in the center. Crack eggs into the well and add salt. Gradually mix with a fork, incorporating flour from the edges. Knead by hand for 8 to 10 minutes until smooth and elastic. Wrap in plastic and let rest for 30 minutes.
02 - Heat olive oil in a skillet over medium heat. Sauté onion until soft, about 3 minutes. Add garlic and mushrooms; cook until mushrooms release moisture and turn golden, approximately 5 minutes. Remove from heat. Stir in shredded chicken, Parmesan, parsley, black pepper, and salt to taste. Allow mixture to cool completely.
03 - Divide rested dough into two equal portions. Roll each piece into a thin sheet, about 1/16 inch thick, using a pasta machine or rolling pin. Maintain even thickness throughout.
04 - Place small mounds of filling, approximately 1 teaspoon each, 1 inch apart on one pasta sheet. Lightly brush edges with water and cover with second sheet. Press firmly around each filling mound to seal. Cut into individual squares and crimp edges with a fork to ensure tight closure.
05 - Heat olive oil in a saucepan over medium heat. Add sliced garlic and sauté until fragrant, about 1 minute. Pour in crushed tomatoes and add sugar, salt, black pepper, and oregano. Simmer uncovered for 15 to 20 minutes until slightly thickened. Stir in torn basil leaves just before serving.
06 - Bring a large pot of salted water to a rolling boil. Gently add ravioli and cook for 3 to 4 minutes, or until they float to the surface. Remove carefully with a slotted spoon to avoid tearing.
07 - Transfer cooked ravioli to serving plates. Spoon warm tomato sauce generously over the top. Garnish with additional grated Parmesan and fresh basil leaves. Serve immediately while hot.