Bring a large pot of water to a boil. Add the squash and cook until just tender, about 6 to 8 minutes. Lift the squash out of the pot with a slotted spoon, set on a plate and set aside.
Add the rigatoni to the pot of boiling water and cook until tender, about 8 to 10 minutes.
Meanwhile, place the oil in a very large, wide skillet set over medium, medium-high heat. Add the kale, Serrano ham, garlic, sage and chilies and cook and stir 3 to 4 minutes, until the kale is wilted. Add the reserved squash and stock and bring to a simmer.
When the pasta is cooked, reserve 1/2 cup of its cooking liquid, then drain well. Add the pasta and reserved cooking liquid and 1/3 cup cheese to the skillet, toss to combine, and serve.
Note: You can use just about any type of cleaned (seeds and inner membranes removed) winter squash in this recipe. Some, such as delicata which has an edible skin, you don’t have to peel before cooking, others, such as butternut, you will.