In a small bowl, combine the mashed beets, ricotta, and milk and stir well with a wooden spoon to combine. Season with salt and pepper, to taste. Allow to cool completely.
Prepare the pasta dough and roll it out to the thinnest setting on a pasta rolling machine. Cut the pasta sheet into 2-inch squares. Place a scant tablespoon of the beet filling on the center of half of the squares and top with the remaining squares, pressing around the edges to seal. Set aside, covered with a damp towel, until ready to use.
Bring 6 quarts of water to a boil and add 2 tablespoons salt. Cook the ravioli in the boiling water until cooked through and tender, about 5 minutes. Drain the ravioli and place in a large serving bowl. Toss with the melted butter and poppyseeds and serve with cheese grated over.
As you expand the well, keep pushing the flour up from the base of the mound to retain the well shape. The dough will come together when half of the flour is incorporated.
Start kneading the dough with both hands, using the palms of your hands. Once you have a cohesive mass, remove the dough from the board and scrape up and discard any leftover bits. Lightly reflour the board and continue kneading for 6 more minutes. The dough should be elastic and a little sticky. Wrap the dough in plastic and allow to rest for 30 minutes at room temperature.
Roll the pasta out on a pasta rolling machine to the desired thickness.