In a covered pasta pot over high heat, bring water to a rapid boil.
Meanwhile, in a large saute pan, heat oil over medium heat. Add pancetta and onion. Cook, stirring, until onion is soft and translucent, about 3 minutes. Add broccoli and cook, stirring, until tender, 3-5 minutes. Add wine, increase heat to high, and cook until reduced by half. Remove pan from heat and set aside.
While sauce is simmering, add kosher salt and spaghetti to the boiling water and cook, uncovered, over high heat until pasta is al dente. Scoop out about 1 cup of the pasta water and set aside; drain pasta.
Return saute pan to medium heat; add 2 tablespoons of the reserved pasta water and increase heat to high. Add spaghetti and toss to coat evenly, adding more pasta water if necessary. Add half the Parmigiano-Reggiano and toss well. Season to taste with salt and pepper.
Transfer to a large serving bowl or platter and sprinkle with remaining cheese; serve immediately.