Preheat oven to 400 degrees.
In a medium Dutch oven or heavy ovenproof pot with a tight-fitting lid, heat oil over medium-high. Add shallots and cook, stirring occasionally, until soft, about 3 minutes. Add garlic and thyme and cook until fragrant, about 1 minute.
Add rice and cook, stirring frequently, until opaque, about 3 minutes; season with salt and pepper. Add wine and cook, stirring, until completely absorbed, about 2 minutes. Add squash and broth; bring mixture to a boil. Stir in kale.
Cover, transfer to oven, and bake until rice is tender and most of liquid is absorbed, about 20 minutes. To serve, sprinkle with Parmesan.