Add the olive oil to a large skillet over medium heat. Once the oil is hot & shimmering, stir in the butternut squash & shallot. Season with 1 teaspoon kosher salt & ground black pepper as desired. Cook, stirring occasionally, until the shallot is fragrant & the butternut squash is fork-tender, 8-10 minutes. Stir in the sage & garlic. Cook 1-2 minutes longer, until fragrant.
Reduce the heat under the skillet to medium-low. Stir in the orzo. Toast the orzo 1-2 minutes, stirring constantly, until nutty & fragrant. Deglaze the skillet by slowly pouring in the white wine while using a wooden spoon to scrape any browned bits on the bottom of the skillet. Let the skillet simmer until the wine is almost completely cooked off, 1-2 minutes.
Add 1 cup of the vegetable broth/stock into the skillet, stirring frequently until the orzo absorbs all of the liquid. Continue adding stock/broth ½ cup at a time. Stir frequently between additions. Start tasting for doneness after 10 minutes – you may not need to use all of the broth. The orzo is ready when it's creamy & cooked through with a nice bite (i.e. al dente) & the butternut squash should break down a little bit, creating a really creamy sauce with a light orange tinge.
Once the orzo is al dente, finish the butternut orzo by stirring in the shredded kale, grated parmesan, butter, & nutmeg. Once the kale is wilted & tender, remove from the heat. Taste & adjust seasonings as needed.