In a large bowl, combine the flour and eggs. Mix until a dough forms. Knead the dough on a floured surface for about 8-10 minutes until smooth. Wrap in plastic wrap and let it rest for 30 minutes.

Roll Out the Fettuccine

Divide the rested dough into four pieces. Roll each piece through a pasta machine until thin (about 1/8 inch thick). Cut into fettuccine strips and dust with flour to prevent sticking.

Prepare the Bolognese Sauce

In a large skillet, heat olive oil over medium heat. Add the onion, carrot, and celery. Sauté until softened, about 5 minutes. Add the ground beef and cook until browned.

Simmer the Sauce

Stir in the crushed tomatoes, red wine, milk, salt, and black pepper. Bring to a simmer and reduce heat. Let cook for at least 30 minutes, stirring occasionally.

Cook the Fettuccine

Bring a large pot of salted water to a boil. Add the fettuccine and cook for 2-3 minutes until al dente. Drain and reserve some pasta water.

Combine and Serve

Toss the fettuccine with the Bolognese sauce, adding reserved pasta water as needed to reach desired consistency. Serve hot, topped with grated Parmesan cheese.