Heat a little oil in a large pot and sauté the onion, carrot, and celery over medium-low heat for about 8–10 minutes, until the vegetables are soft. This is the sofrito and forms the base of the sauce.
Add the garlic and sauté briefly.
Add the ground chicken and cook, breaking it up with a spoon, until fully cooked.
Make a little space in the center of the pan and add the tomato paste. Cook for about 1 minute to mellow its acidity.
Next, add the tomato sauce, bouillon cube, balsamic vinegar, smoked paprika, Italian seasoning, bay leaf, Worcestershire sauce, and milk.
Let the sauce simmer gently for about 1 hour, uncovered. Stir occasionally to allow the flavors to develop.
Meanwhile, cook the pasta according to the package instructions.
After simmering, remove the bay leaf from the sauce. Season with additional salt and/or pepper if needed.
Serve the pasta with the chicken Bolognese sauce and, if desired, finish with some grated Parmesan cheese.