Make a roux by melting the butter in a saucepot over medium heat. Add the flour and stir lightly until incorporated. The roux should look like "wet sand"; if not, adjust with more butter or flour as necessary. Add the milk and cook and thicken to make a bechamel sauce. (The sauce should be slightly thicker than heavy cream.) Reserve and keep warm.
Bring a pot of salted water to a boil; prepare an ice-water bath. Blanch the broccoli florets in the boiling water and immediately transfer to the ice water to stop the cooking process. When cool, drain and set aside.
Cook the pasta according to the package instructions. Before draining, set aside 1 cup of the pasta water. Drain the pasta and coat with a bit of oil to prevent the pasta from sticking together. Reserve.
Heat a saute pan over medium-low heat. Add the grapeseed oil, garlic and onions and cook until transparent. Add the sun-dried tomatoes and zucchini and sweat down a bit. Add the broccoli florets followed by the bechamel sauce and pasta. Toss to combine, adding a little of the reserved pasta water if the sauce seems too thick. Mix in the Parmesan. Add the chives, 2 tablespoons salt and the pepper and toss to combine.
Transfer to a serving bowl and garnish with the chopped parsley and more Parmesan.