01 - Mound the flour on a clean work surface and create a deep well in the center. Crack the eggs into the well and add the salt. Using a fork, gently beat the eggs while gradually pulling in flour from the inner walls of the well. Continue mixing until a shaggy dough forms, then knead firmly for 7 to 8 minutes until the dough is smooth, elastic, and springs back when pressed. Wrap tightly in plastic wrap and let rest at room temperature for 20 minutes to relax the gluten.
02 - In a medium mixing bowl, combine the finely chopped chicken, ricotta cheese, Parmesan cheese, minced garlic, parsley, and nutmeg. Season generously with salt and freshly ground black pepper. Stir until all ingredients are evenly distributed and the mixture holds together when pressed. Taste and adjust seasoning as needed.
03 - Unwrap the rested dough and divide it into four equal portions. Working with one piece at a time while keeping the others covered, roll the dough out to approximately 1/16-inch thickness using a rolling pin or pasta machine. Cut the sheet into 2-inch squares or circles using a knife, pasta cutter, or round cutter. Place a rounded teaspoon of filling in the center of each piece. Fold the dough over the filling to form a triangle or half-moon, pressing firmly to seal out any air pockets. Bring the two bottom corners together and press to join, creating the classic tortellini shape. Transfer finished tortellini to a lightly floured baking sheet and repeat with remaining dough and filling.
04 - Bring a large pot of generously salted water to a rolling boil over high heat. Carefully drop the tortellini into the water in batches to avoid crowding. Cook for 3 to 4 minutes, or until the pasta floats to the surface and the edges are tender. Remove with a slotted spoon and transfer directly to the cream sauce.
05 - While the tortellini are cooking, melt the butter in a large saucepan over medium heat. Pour in the heavy cream and bring to a gentle simmer, cooking for 2 to 3 minutes until slightly thickened. Reduce the heat to low and stir in the Parmesan cheese, continuing to stir until fully melted and the sauce is smooth and velvety. Season with freshly ground black pepper to taste.
06 - Gently toss the freshly cooked tortellini in the warm cream sauce until evenly coated. Divide among warmed serving plates or bowls. Finish with an extra sprinkle of Parmesan cheese and a scattering of freshly chopped parsley. Serve immediately while hot.