Dust 2 large sheet pans heavily with cornmeal. Set aside.
Mound 4 cups of the flour in the center of a large wooden cutting board. Make a well in the middle of the flour and add three eggs and milk mixture. Using a fork, beat together the eggs and milk mixture and begin to incorporate the flour, starting with the inner rim of the well. As you expand the well, keep pushing the flour up to retain the well shape. The dough will come together when half of the flour is incorporated.
Start kneading the dough, using the palms of both hands. Once you have a cohesive mass, remove the dough from the board and scrape up and discard any crusty bits. Lightly flour the board and continue kneading for six more minutes. The dough should be elastic and firm. Wrap the dough in plastic and allow to rest for 30 minutes at room temperature. Do not skip the kneading or resting portion of this recipe, as they are essential to a light pasta.
Cut the dough into 6 equal portions and roll each into a 1-inch thick log. Run each log through a meat grinder set to the smallest extrusion size using the plunger to push the dough. As the pasta exits, cut it into 12-inch pieces and let it fall onto prepared sheet pan. Shake the pasta in the cornmeal, gently separating the strands while rolling them in the cornmeal. Repeat with the remaining dough
Over medium heat, heat the olive oil in an oven-proof pan until hot but not smoking. Once the pan is ready, add the hare legs and sear until lightly browned on the outside, but not cooked through, about 6-8 minutes each side. Remove the browned meat from the pan. Add the onion, carrots and celery and sauté until the vegetables begin to soften and turn light golden brown, about 5 to 10 minutes. Add the tomato paste and cook for another 10 minutes. Add red wine, stock, herbs, season to taste with salt and pepper and bring to a boil. Cook for 10 minutes and then return the hare legs to the pan, bring to a boil, lower heat to a simmer, cover and braise in the oven for 1½ hours or until the meat comes off easily from the bone. Let cool and remove the meat from the bones and pull into ½ inch pieces. Place meat back into juices and simmer for 20 minutes.