Heat the olive oil and butter in a large saucepan over medium-low heat. Add the onion and some salt and cook until translucent. Add the red pepper, celery and carrots, and saute for 10 minutes until the carrots are soft. Add the garlic and mushrooms and give a stir, then add the lamb. Break up the lamb while stirring, and continue to cook until it's no longer pink, about 10 minutes. Add the tomato paste and the milk, stirring until the milk has evaporated. Drain the fire-roasted tomatoes (it's fine if a bit of liquid remains, but drain the majority of it) and add them to the pot. Season generously to taste with salt and pepper.
The longer this simmers, the more the flavors will come together. But it tastes perfectly good if you let it cook for an extra 15 minutes from this point forward while preparing some pasta. Just before serving, add the sliced basil and some shaved or grated parmigiano reggiano.