Bring large pot of water to a boil. Add beets, along with greens and stems. After 2 minutes, transfer greens and stems to a bowl of ice water; drain. Continue to boil beets until tender, another 8-10 minutes. Remove beets from boiling water and allow to cool. Peel and dice beets.
Heat large saucepan over medium heat. Toast pine nuts until lightly golden, about 4 minutes. Transfer to a small bowl and set aside.
Add oil to same saucepan. Once oil is hot, add pancetta and cook for 3 minutes on medium-high heat until it begins to brown. Add onions and cook together for another 8 minutes, until onion is golden brown. Stir in garlic and salt, cooking until onions are softened, then add beets and greens.
Meanwhile, bring a large pot of salted water to a boil and cook pasta according to package instructions. Toss beet mixture with hot pasta and cook together for 2 more minutes to marry flavors. Serve topped with toasted pine nuts and Parmigiano-Reggiano.