NOTE: Remember that you can use my LENTIL BOLOGNESE recipe linked above in the post for this to be vegetarian!
Preheat the oven to 400 degrees F. Brush the peppers (inside and outsides) with 1 tablespoon of the olive oil and sprinkle with a big pinch of salt and pepper. Place the peppers on a baking sheet and roast for 15 to 20 minutes.
While the peppers are roasting, make the bolognese.
Heat a large pot over medium heat and add the remaining tablespoon of olive oil. Add in the onions with a pinch of salt and pepper and cook, stirring occasionally, until softened, about 5 to 6 minutes. Add in the garlic and mushrooms. Stir and cook for another 5 or 6 minutes, until the mushrooms soften. Add in the turkey and break it apart with a wooden spoon. Brown it, stirring and breaking it apart, until it's cooked through, about 6 to 8 minutes. Stir in the tomato paste, dried basil, oregano, pepper flakes and brown sugar. Cook for 2 more minutes.
Add in the wine, tomatoes and parmesan. Bring the mixture to a boil then reduce to a simmer and cover, cooking for 15 minutes (or even longer if you wish!). You can make this ahead of time, FYI!
Remove the peppers from the oven. Fill the peppers with the bolognese mixture. Top with the grated cheese. Stick them back in the oven for 15 minutes until the cheese is melty. Remove and top with parmesan before serving.