Heat the olive oil in a 4-quart / 3.8L Dutch oven over medium heat. Add the onion, carrots, and celery and cook for 6 minutes, stirring, until softened.
Add the garlic and cook for 30 seconds until fragrant.
Add the ground turkey, breaking it up with a wooden spoon. Cook for 7 to 8 minutes until no longer pink and the internal temperature reads 165°F / 74°C.
Stir in the tomato paste and cook for 1 minute, until it darkens slightly.
Add the rinsed lentils, crushed tomatoes, broth, oregano, basil, bay leaf, red pepper flakes, salt, and black pepper. Stir well and bring to a simmer.
Reduce the heat to low, partially cover the pot, and simmer for 28 to 32 minutes, stirring every 10 minutes or so, until the lentils are tender and the sauce coats the back of a spoon.
Remove the bay leaf. Stir in the milk and simmer uncovered for 5 more minutes to mellow the acidity.
Taste and adjust salt and pepper. If the sauce looks thin, simmer uncovered a few extra minutes; if it's too thick, loosen with a splash of broth.
Serve hot over pasta or on its own in bowls, topped with grated parmesan.