Bring a large pot of water to boil for the pasta.
In a small saucepan, heat the wine, garlic and saffron over medium until the wine is reduced by half, about 5 minutes. Add the cream and season with salt and white pepper. Reduce the heat to medium-low and simmer gently, stirring occasionally, until the sauce is reduced by about half, about 10 minutes.
In a large skillet, heat the olive oil, three turns of the pan, over medium. Add the pancetta and cook, stirring often, until lightly browned, about 5 minutes.
Salt the boiling water, add the pasta and cook to al dente. Add a ladleful of the starchy pasta water to the pancetta in the skillet. Drain the pasta and transfer to the skillet. Discard the garlic from the saffron sauce; add the cheeses and stir until smooth. Pour the saffron sauce over the pasta and toss to combine. Adjust the seasoning and top with more cheese and the parsley.