In a large non-stick skillet, sweat the finely chopped onion over low heat in butter (or oil). Once it begins to soften, pour in the warm milk and let it reduce.
Add the diced prosciutto crudo and sauté until the fat starts to render and melt. Increase the heat slightly to brown it for a few moments, then stir in the warm tomato passata and season with black pepper. Cover and cook over medium-low heat for about 15 minutes, or until the sauce has thickened.
Meanwhile, cook the tagliatelle in a large pot of boiling salted water. Drain when al dente and toss directly with the prepared sauce.