This was one of our courses on Valentines day. I really enjoyed this dish and thought I'd share.
First roast some beets. You can drizzle them skin on with a bit of oil and wrap them in foil and toss them in the oven until tender, or you can put them in a pan with a bit of water, cover with foil and bake them that way. You won't need many. Just use your judgement on how much filling you will need to fill the amount of pasta for however many people.
Once they are cooled, toss them in the food processor until uniformly ground. For the best results wrap them in cheesecloth and hang them overnight over a bowl to catch the excess liquid. Place your beet pulp into a mixing bowl and season aggressively to taste with salt and pepper. Add a bunch of shredded parmesan to taste, and some fresh mint chiffonade. Add some bread crumbs, a little at a time while mixing to thicken up the mixture. Try to go for the consistency of ricotta cheese. Once you have it where you want it and tasting good, add some egg. You won't need much, for say, 2 cups of filling a third of a beaten egg should be plenty. Put your filling aside.
Make your pasta dough. This recipe will make way more pasta than you need, so make some fettuccine or something.
6 large egg yolks
1 large egg
tsp Olive oil
Decent pinch of salt
1 3/4 cups AP flour (00 is better but more difficult to find.)
Make a well in the center of your flour, mix all your wet ingredients together and pour into the well. Using a fork or spoon, whisk from the center slowly incorporating flour from the edges until the dough begins to come together, it will be kind of stick and crumbly. Begin kneading your dough until it comes into a ball and is smooth and elastic. 4-5 minutes should be fine. Wrap up your dough and let it rest for 20-30 mins. While your dough is resting make your sauce.
Peel a bunch of Cippolini onions halve or quarter them and toss them in a pan and cover them with chicken stock. Simmer slowly until the onions are tender. You don't really want any color or carmelization. Strain the onions and puree them in a blender. Add a bit of water to thin it to a sauce like consistency and season to taste with salt.
Now make your pasta. Cut mabye a third of the pasta off of your ball and flatten it out a bit with a rolling pin. Run it through your pasta machine a few times until you get a nice even square and then start raising the number until you get to 7 and you have a nice long sheet. Lay it down on your work area going from right to left and brush the lower half of the dough with egg wash. Get a piping bag and fill it with your beet mixture. Pipe a tube of filling at the very bottom of your sheet all the way across from right to left or vice versa. Now from the bottom roll your entire sheet upwards over the filling twice. Now using your two index fingers pinch downwards on the tube from right to left in one inch increments all the way across your sheet. Using a knife or a pasta cutter cut vertically through the indentations made by your fingers. You will now have several little sealed pouches of filling. Trim the excess dough from the tops to the desired length, you can re roll the scraps later if you want. You should be left with something that looks like this:
Those aren't the beet agnolotti, just a pic I pulled off the internet.
To finish, cook the pasta heat the sauce add some more fresh mint chiffonade and toss your cooked pasta in it. Top with some more parm and dig in.
Even if you don't make the beet filling, learn to make agnolotti, they are by far the easiest filled pasta to make. Here is a youtube video to help you visualize my instructions. http://www.youtube.com/watch?v=3ceKG_0_xdQ&feature=related