Place a large pot of salted water on to boil for the gnocchi. Roughly chop the butternut squash into ½ inch pieces. Trim the bottom inch off the stems of the broccoli rabe and discard, then chop the remaining stalks into 1 inch pieces. Finely chop the parsley leaves.
Toast the nuts
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.
Cook the vegetables
Return the skillet with the butter to medium-high heat. Add the chopped butternut squash, chopped broccoli rabe, and a good pinch of salt and pepper. Toss to coat then cook, stirring occasionally, until butternut squash is fork-tender and everything is well browned, about 4 to 6 minutes.
Cook the gnocchi
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. Remove from heat and add the chopped parsley. Toss to combine, adjust seasoning with salt and pepper as needed. Divide the butternut squash gnocchi between large shallow bowls or plates. Top with toasted hazelnuts.