01 - Mound flour on a clean work surface and create a well in the center. Crack eggs into the well and add salt. Gradually incorporate flour into eggs using a fork, then knead by hand for 8-10 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. Fold in chicken, Parmesan, parsley, pepper, and salt. Allow to cool completely.
03 - Divide rested dough into two equal portions. Roll each piece into thin sheets, approximately 1/16 inch thick, using a pasta machine or rolling pin.
04 - Place small mounds of filling, about 1 teaspoon each, spaced 1 inch apart on one pasta sheet. Lightly brush edges with water, cover with second sheet, and 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, sugar, salt, pepper, and oregano. Simmer uncovered for 15-20 minutes until slightly thickened. Stir in torn basil just before serving.
06 - Bring a large pot of salted water to a rolling boil. Gently drop ravioli into water and cook for 3-4 minutes, or until they float to the surface. Remove carefully with a slotted spoon.
07 - Transfer cooked ravioli to serving plates. Spoon warm tomato sauce over the top. Garnish generously with grated Parmesan cheese and fresh basil leaves. Serve immediately while hot.