Heat oil in a large braising pan or Dutch oven over medium heat. Add the diced onion, celery, and carrots. Sauté until softened, then add the garlic and chili flakes and cook for another minute until fragrant.
Remove the vegetables from the pan and set aside.
Add the ground beef to the same pan. Break it apart and cook until browned.
Add the tomato paste to the browned beef and stir well. Cook for a few minutes, allowing the tomato paste to toast and deepen to a rich red color.
Return the sautéed vegetables to the pan. Pour in the chicken stock and add the fresh thyme, Italian seasoning, brown sugar, and black pepper. Stir to combine. (If you want a long-simmered bolognese and to cook the pasta separately, see notes below!)
Bring the sauce to a simmer and cook for 10 minutes.
Taste the sauce and adjust the seasonings as needed.
Add the fettuccine directly to the sauce and cook until tender, about 15–20 minutes, stirring occasionally. Add more chicken stock as needed while the pasta cooks to keep the sauce from getting too thick.
Once the pasta is tender and the sauce has thickened, remove the thyme sprigs and serve!