Grate the beet with a microplane into a fine paste. Mix it in with the flour and eggs in a bowl or in the food processor. Mix well to combine and knead for 5 minutes until a nice thick dough is formed. Add more flour as needed. Wrap in plastic and allow to rest for 30 minutes in the fridge.
Cook the lamb in a frying pan with a little oil until browned. Season with salt and pepper while it is cooking. Pour into a mixing bowl and allow to cool for 5 minutes. Add in the rest of the filling ingredients. Stir well to combine.
Roll 1/3 of your pasta dough through the pasta machine at the widest setting. Fold over and repeat 4 or 5 times until the dough is smooth. Roll the dough thinner moving the machine 2 notches thinner each time you roll it, repeating until you get to the 3rd thinnest setting.
Place a tablespoon of filling on to the pasta sheet and repeat until the sheet is dotted with filling on one half of the sheet. Brush the dough with some water. Fold the other half of the sheet over onto the filling and gently seal the pasta on all sides of the filling. You want to make sure most of the air is removed from the pasta. Use a pasta cutter to cut the ravioli into a square and really seal in the filling. Place the finished pasta onto a sheet or towel with some flour. Repeat until you run out of filling or dough.
Separate the beet greens from the stems. Chop up the greens. Slice the stems into small pieces.
Cook the onion and beet stems in some oil for about 5 minutes. Add in the garlic and cook 2 minutes. Add in the cream and tomatoes and cook 20 minutes until thickened and smooth. Stir in the beet greens and cook another 2 minutes.
Boil some water and cook your ravioli about 5 minutes until tender. Add directly to the sauce and stir to combine. Serve with parmesan and black pepper.