Place a large pot of salted water on to boil for the gnocchi. Trim the bottom inch from the stems of the broccoli rabe, then chop the remaining stalks into 1 inch pieces. Roughly chop the hazelnuts.
Place a large nonstick skillet over medium heat with the butter. Once melted, add the hazelnuts and cook until fragrant and lightly browned, about 3 to 4 minutes. Using a slotted spoon, transfer the toasted nuts to a plate, reserving the butter in the skillet.
Return the skillet with the butter to medium-high heat. Add the sage leaves, kabocha squash cubes, chopped broccoli rabe, and a good pinch of salt and pepper. Toss to coat then cook, stirring occasionally, until kabocha squash is fork-tender and everything is well browned, about 4 to 6 minutes.
Add gnocchi to the boiling water and cook until they float to the surface, about 3 to 4 minutes. Reserve ⅓ cup pasta water and drain. Add the gnocchi to the skillet with the vegetables, and cook, tossing occasionally, until browned in places, about 4 to 6 minutes. Add reserved pasta water and white balsamic vinegar to the skillet and cook until most of the water evaporates, less than 1 minute.
Add the dried cranberries to the skillet. Toss to combine and cook until just heated through, about 1 to 2 minutes. Taste, and adjust seasoning with salt and pepper as needed. Divide the kabocha squash gnocchi between large, shallow bowls or plates. Top with toasted hazelnuts.