Lower the oven heat to 350º F.
Heat one tbsp of the butter in a large pan or dutch oven over medium-high heat. Once hot, add the onion and garlic and sauté until softened, about 5 minutes. Add the kale, a pinch of salt, and an additional tbsp of butter and sauté until the kale is deep green and slightly wilted.
Add the rice, broth, and thyme, stirring to combine. If using a dutch oven, transfer to the oven. If using a pan, pour contents into an oven-safe dish and then transfer to the oven.
Bake for 30-40 minutes, or until the rice is creamy and cooked al dente.
Add the water or broth, cheese, and shallots, then stir until well-combined, 1-2 minutes. Taste and season with salt and pepper (I used a lot of salt!).
Top with the delicata squash and serve hot.