In a large nonstick skillet, heat the olive oil over medium-high heat. Season the pork with salt and pepper, then add to the pan and cook, turning once, until golden, about 8 minutes. Transfer to a work surface and tent with foil. While the pork is cooking, in a bowl, combine the butternut squash, apples and onion with the butter; season with salt and pepper.
Add the apple mixture to the pan and cook, stirring occasionally, until the squash is just fork-tender, 3 to 5 minutes; transfer back to the same bowl. Add the cabbage and kale to the pan and cook, stirring, for 2 minutes. Return the apple mixture and pork to the pan, add the cider, partially cover and simmer until the pork is cooked through, 5 to 8 minutes. Season with salt and pepper.
Transfer the pork to a work surface and let rest for 5 minutes before slicing. Serve with the vegetable.