Preheat the oven to 375 degrees . In a large pot, heat the EVOO over medium heat. Add the onion and cook until softened, 5 minutes. Add the mushrooms and cook until softened and most of their liquid has evaporated, about 5 minutes.
Sprinkle with the flour and cook, stirring, for 2 minutes. Increase the heat to medium- high, add 1 cup broth and cook, stirring, until sauce is smooth, about 2 minutes. Stir in the milk and bring to a boil; lower the heat and simmer, stirring, until the sauce has thickened, 15 to 20 minutes. Remove from the heat.
Meanwhile, in a large pot of boiling, salted water, cook the noodles until al dente. Drain.
Using a food processor, puree the cauliflower with the remaining 1/4 cup broth. Stir the cauliflower into the sauce and season with salt and pepper. Gently fold in the noodles and turkey. Transfer tetrazzini to a 9-by-13-inch foil-lined baking dish and sprinkle the breadcrumbs on top. Bake until the edges are golden-brown, about 30 minutes. Top with the parsley.