Preheat the oven to 400 degrees F and line a baking sheet with parchment paper.
Bake the squash. Spray the cut sides of the squash with olive oil and sprinkle with salt and pepper. Place them cut-side down on the baking sheet and bake for 15 minutes, then flip and bake another 30-40 minutes, until fork tender.
Meanwhile, while the squash bakes make the rice. In a small lidded saucepan, combine the rice, cooking liquid and salt and place over high heat. Bring to a boil, turn the heat down to low and simmer for 35-40 minutes, until tender. Drain any excess liquid and set aside.
Heat 1 tablespoon olive oil in a medium skillet over medium heat. Crumble the sausage into a skillet and cook until lightly browned, but still pink in some areas.
Add the mushrooms, garlic and a pinch of salt, and cook, stirring until the mushrooms are soft, about 2 minutes. Stir in the kale, and cook until completely wilted, about 2 minutes.
Add the cranberries and 1 tablespoon of the chopped thyme and stir to combine. Season with salt and pepper and remove from heat. Toss with the prepared rice.
Once the squash is done, set it aside until cool enough to safely handle.
Cupping the sides of the squash with one hand so that it doesn’t tear, spoon out some of the flesh, leaving a 3/4” border around the sides and bottom.
Dice the remaining squash in small pieces and mix with the rice and sausage.
Divide the sausage mixture between the hollowed out squash halves and fill to the top, mounding in the middle if there is extra. Return to the oven to cook for another 5 minutes.