For the pasta dough: Whisk the 00 or all-purpose flour and the semolina flour in the bowl of a stand mixer to combine. Make a well in the center.
Combine the whole eggs, yolks, milk and olive oil in a small bowl and pour it into the well. Using the dough hook, mix on low speed until the dough just starts to come together, then increase the speed to medium and mix for 5 minutes.
Lightly flour your work surface and turn the dough onto it. Knead the dough by hand until it is smooth and elastic, and springs back when you press it with your finger, about 10 minutes. Wrap the dough in plastic wrap and refrigerate for 1 hour.
For the filling: Combine the ricotta, mascarpone and Parmesan in a small bowl. Put the mixture in a pastry bag and refrigerate until needed.
For the ragu: Put the beef stock, red wine and porcinis in a small saucepan. Bring to a boil over high heat, reduce the heat and let the mixture simmer.
Heat the olive oil in a Dutch oven over medium-high heat. Add the beef, hot and sweet Italian sausages and prosciutto and cook, breaking up the beef and sausage with a whisk, until well browned, about 10 minutes. Season with some salt and pepper.
Stir the tomato paste into the meat, then stir in the rosemary, thyme, garlic, bay leaves and onions and cook, stirring, until the onions soften slightly, about 5 minutes.
Strain the beef stock mixture into the meat. Add the tomatoes and bring the mixture to a boil. Reduce the heat so the mixture simmers and cook, stirring occasionally, until thickened, about 45 minutes. Add the cream and continue to simmer another 15 minutes or so. Stir in the parsley. Taste and adjust the seasoning if necessary.
To fill and finish the agnolotti: Cut the dough into 4 pieces. Set a pasta roller at the widest setting.
Pass the first piece of dough through the roller, fold it in half and run it through again. Fold the dough in half again, dust it with flour, and run it through the roller again. Reduce the width setting on the roller and run the dough through. Continue to run the dough through, reducing the width with each pass, until the pasta is thin enough so that you can see the shadow of your hand through the other side. Lightly flour your work surface and lay the pasta sheet on top.
Pipe 1 teaspoon of filling about 1 inch from the edge. Continue to pipe additional teaspoons of filling 1 inch apart, from one end to the other. Fold the dough over so that it extends about an inch past the filling (it won¿t extend to the opposite edge), press to seal the long edge and then trim the excess dough from the sealed side. With your fingers perpendicular to the table, pinch between the mounds to seal the filling in. Then use the cutter to cut between each mound, through the pinch, creating little purses. Dust the finished agnolotti with flour. Refrigerate until ready to cook. Repeat the process with the 3 remaining pieces of dough and the filling.
Bring a large pot of salted water to a boil over high heat. Add the agnolotti, stir and, when they float to the surface, leave them in the water for an additional minute. Use a spider or slotted spoon to transfer the agnolotti to a large bowl. Ladle over some ragu, toss, drizzle with olive oil and sprinkle with grated Parmesan. Serve immediately.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.