Bring a large pot of salted water to a boil. Add the gnocchi and cook until they float to the surface and are tender, usually 2 to 3 minutes. Drain and set aside.

While the gnocchi cooks, heat a large skillet over medium heat. Add the olive oil and butter. Once the butter melts, add the sliced chicken sausage and sauté until nicely browned at the edges, about 4 to 5 minutes.

Toss in the diced onion and minced garlic. Cook until the onion is translucent and the garlic is fragrant, about 2 minutes. Stir in the chopped kale and let it wilt slightly, 1 to 2 minutes.

Pour in the chicken broth and give everything a good stir. Let it simmer gently for 2 minutes to marry the flavors.

Reduce heat to medium-low. Add the heavy cream and grated parmesan. Stir until the sauce thickens a bit and coats the gnocchi and greens. If the sauce looks too thick, loosen it with a splash more broth or water.

Season with salt and pepper to taste. Add the drained gnocchi to the skillet and gently toss to combine. Cook just until everything is heated through, about 2 minutes more.

Taste and adjust with a final pinch of salt and cracked pepper. Serve warm, with extra parmesan on the side if you like.