01 - Mound flour on a clean work surface and create a deep well in the center. Crack eggs into the well and add salt. Using a fork, gradually incorporate flour into eggs until a shaggy dough forms. Knead by hand for 8 to 10 minutes until smooth and elastic. Wrap tightly in plastic wrap and let rest at room temperature for 30 minutes.
02 - Heat olive oil in a skillet over medium heat. Sauté chopped onion for 3 minutes until translucent. Add minced garlic and chopped mushrooms; cook for 5 minutes until mushrooms release moisture and turn golden. Remove from heat and let cool slightly. Stir in shredded chicken, grated Parmesan, chopped parsley, black pepper, and salt to taste. Allow filling to cool completely before assembling ravioli.
03 - Cut rested dough in half and work with one portion at a time, keeping remaining dough covered. Roll dough into a thin sheet approximately 1/16 inch thick using a pasta machine or rolling pin. Aim for even thickness throughout to ensure uniform cooking.
04 - Place small mounds of filling, about 1 teaspoon each, onto one pasta sheet spaced 1 inch apart. Lightly brush water around each mound. Cover with second pasta sheet and press firmly around filling pockets to expel air. Cut into individual squares using a knife or ravioli cutter. Crimp edges with a fork to ensure tight seal.
05 - Heat olive oil in a saucepan over medium heat. Add sliced garlic and sauté for 1 minute until fragrant but not browned. Pour in crushed tomatoes and add sugar, salt, black pepper, and dried oregano. Reduce heat to low and simmer uncovered for 15 to 20 minutes until sauce thickens slightly. Stir in torn fresh basil just before serving.
06 - Bring a large pot of salted water to a rolling boil. Gently drop ravioli into water, being careful not to overcrowd the pot. Cook for 3 to 4 minutes until ravioli float to the surface. Remove carefully with a slotted spoon, draining excess water.
07 - Arrange cooked ravioli on warm serving plates. Spoon hot tomato sauce generously over pasta. Finish with additional grated Parmesan cheese and fresh basil leaves. Serve immediately while hot.