Cook the gnocchi according to the package directions. Reserve ½ cup gnocchi cooking water, and drain. Set aside.
Meanwhile, heat the oil in a 12-inch nonstick skillet over medium heat until hot. Add the squash and salt and cook, stirring occasionally, until tender and browned, about 10 minutes. Increase the heat to medium-high, and add the butter, garlic, and sage and cook until the foaming subsides, 1 to 2 minutes.
Add the gnocchi, reserved cooking water, shallot, and pepper, and stir until thoroughly combined. Transfer to large serving bowl. Sprinkle with the parmesan, and serve.