Prepare the ingredients. Peel and cut the butternut squash into ½-inch cubes. Dice the onion, mince the garlic, chop the sage, and remove the beef sausage from its casings.
Brown the sausage. Heat the olive oil in a large skillet over medium-high heat. Add the beef sausage and break it into small pieces with a wooden spoon. Cook for 5–7 minutes, or until browned and completely cooked through. Transfer to a plate.
Cook the squash. Add the cubed butternut squash to the same skillet. Cook for 6–8 minutes, stirring occasionally, until it begins to soften and develops lightly golden edges.
Add the aromatics. Stir in the diced onion and cook for another 3–4 minutes until softened. Add the garlic, sage, and thyme and cook for about 1 minute, just until fragrant.
Cook the gnocchi. Add the potato gnocchi to the skillet and cook according to the package directions. If using gnocchi suitable for pan-frying, leave it undisturbed for a few minutes at a time to develop lightly crisp, golden edges.
Make the creamy sauce. Return the cooked beef sausage to the skillet. Pour in the heavy cream and chicken broth, gently stirring everything together.
Simmer. Reduce the heat to medium-low and simmer for 3–5 minutes, stirring occasionally. The squash should become completely tender and the cream sauce should begin to thicken.
Add the Parmesan. Stir in the freshly grated Parmesan until melted and the sauce is smooth and creamy. Add a splash of chicken broth if the sauce becomes thicker than you prefer.
Season. Season the Butternut Squash Sausage Gnocchi with salt, black pepper, and optional red pepper flakes. Taste and adjust the seasoning as necessary.
Garnish and serve. Remove the skillet from the heat and sprinkle with fresh parsley. Add extra freshly grated Parmesan if desired and serve immediately.