While the pasta is working, in a heavy pot, heat the EVOO, 2 turns of the pan, over high heat until smoking. Stir in the veal to brown slightly then stir in the sausage, crumbling the meat as it cooks. Add the carrot, celery, onion, garlic and sage; season generously with salt and pepper. Cover and cook the vegetables, stirring occasionally, until softened, 3 to 5 minutes. Stir in the tomato paste, then stir in the wine to deglaze, scraping up the browned bits from the bottom of the pan.
Remove the mushrooms from their soaking liquid and chop. Stir into the ragu with their strained liquid, leaving any sediment behind. Stir in the milk, lower the heat to medium-high and cook to thicken.
Stir the reserved 1 cup pasta cooking water into the ragu. Add the pasta and toss to coat. Top with a liberal amount of cheese.