In a heavy-bottomed casserole or Dutch oven, heat the olive oil until smoking. Season the Partridge with salt and pepper and cook until the meat has some color but is not cooked through. With a slotted spoon, remove the meat and transfer to a plate lined with a paper towel.
Add the onion, carrot, garlic and celery and cook until softened, about 7 to 9 minutes. Add the tomato paste and stir to distribute evenly. Add the wine and bring to a simmer. Add the partridge, lower the heat, cover and allow to simmer for 1 hour. Season with salt and pepper and set aside.
Fill a large pot with 6 quarts water and add 2 tablespoons salt. Cook pici about 4-6 minutes. Heat the sauce, drain pasta and toss in pan. Toss to coat, top with Pecorino Toscano and serve immediately.