Remove the Italian sausage from its casings and slice it into bite-sized rounds. Heat the olive oil in a large, high-sided skillet over medium heat. Once the oil is hot, add the sliced sausage and cook for about 4 minutes on one side without turning, allowing it to brown nicely. Flip the sausage pieces over and cook for 2 more minutes until both sides are browned.
To the same skillet with the browned sausage, add the uncooked potato gnocchi, heavy cream, and chicken broth. Stir well and bring the mixture to a boil over medium heat. Cover the skillet and allow the gnocchi to cook in the sauce for about 5 minutes, or until the gnocchi are just tender. Make sure to stir occasionally to prevent sticking.
Add the butternut squash puree and minced garlic to the same pan with the gnocchi and sausage mixture. Raise the heat to bring the sauce to a gentle boil again, then reduce to low-medium. Stir everything well to combine and let cook for about 3 minutes or longer, until the gnocchi are cooked through, the garlic is softened to your liking, and the sauce has thickened to your preferred consistency. You can cook a bit longer if you want a thicker sauce. Remove the skillet from heat when finished.
Stir in half of the fresh chopped sage and half of the fresh thyme leaves to the skillet. Season to taste with salt and coarsely ground black pepper. Taste the sauce before adding salt, as the sausage may be salty enough. I like to taste the sauce at this stage and adjust the seasonings for perfect balance—sometimes a little more pepper brings out the richness of the squash.
When serving, spoon the gnocchi and sausage mixture onto plates and top with the remaining chopped fresh sage and fresh thyme leaves. This adds a burst of herbal aroma and gives a beautiful, fresh finish to the dish.