Heat oil in a large pan and saute the onions and carrots until translucent, about 5 minutes. Add the garlic, thyme and chile flakes. Saute for 2 more minutes. Add 1/2 cup veal stock into the vegetable mixture. Add the ground beef, veal and pork, stirring and adding more veal stock when necessary to keep the meat moist. Sprinkle with salt and pepper. Cook for about 10 minutes.
Add the milk and stir. Continue cooking until half of the liquid has evaporated, about 2 minutes. Add the tomato paste, the remaining veal stock and continue cooking until desired thickness. Adjust the seasoning.
Cook the pasta in salted boiling water, about 8 minutes. Drain and mix with the butter, and then add the sauce, chives and basil. Mix well. Serve with grated Pecorino cheese.