In a 6 or 8-quart, heavy-bottomed saucepan, heat the olive oil over medium heat. Next, add the onions, celery, and carrots and sweat over medium heat until the vegetables are translucent, but not browned, about 6 minutes.
Add the beef and stir it into the vegetables. Brown the beef over high heat, stirring to keep it from sticking to the pan.
Add the red wine, and reduce over high heat until almost evaporated. Then, add the tomato paste, and mix thoroughly for a few minutes. Add the flour and stir for 2 to 3 minutes. Cover the contents of the pan with the beef stock, add the thyme, and add the salt and pepper to taste. Bring to a boil, and then simmer over medium-low heat for 30 minutes.
In a large pot, bring 6 quarts of water to a boil and add 2 tablespoons of salt. Cook the pasta, about 6-9 minutes.
Transfer 2 cups of the bolognese sauce to a 12 or 14-inch sauté pan, and heat gently over medium heat with 1 tablespoon of butter.
Drain the pasta, add it to the 2 cups of bolognese and butter, and toss over medium heat until the pasta is coated, about 1 minute.
Divide evenly among 6 to 8 warmed bowls. Grate Parmigiano-Reggiano over each bowl and serve immediately.