Bring a pot of salted water to a boil. Meanwhile, melt the butter in a medium skillet over medium heat. Add the shallot and saffron and cook, stirring occasionally, until the shallot is softened, about 2 minutes. Add the cream, 1/4 teaspoon salt, and pepper to taste; increase the heat to medium high and simmer until slightly thickened, about 2 minutes. Stir in the lemon juice and vanilla.
Add the pasta to the boiling water and cook as the label directs. Remove 1/4 cup cooking water, then drain the pasta and transfer to the skillet with the sauce. Add the reserved cooking water, the parmesan and half of the chives and toss to coat. Serve topped with the lemon zest, remaining chives and more cheese.