Preheat oven to 400°. Place squash cut side up and brush with olive oil. Sprinkle with salt and pepper and bake for 30 minutes. Then flip over so they are cut side down and roast for another 15 minutes. Then remove from oven. Reduce heat to 350°. While those are baking, make the stuffing.
In a large skillet, over medium-high add 1 tbsp olive oil and let it get really hot. Then add the sage leaves. Let fry for a minute and then add the sausage. Break up with a wooden spoon and cook until nice and browned. Remove from pan.
Reduce heat to medium. To the same pan, add the mushrooms. Let cook for a few minutes and spoon out the initial juice they release. Then add in the shallots, garlic, thyme, salt and pepper. Cook for about 4-5 minutes until shallots are softened. Stir in rice and heavy cream. Then add 1/2 cup of the cheese. Stir to combine and let simmer for a couple minutes.
Flip squash cut side up and fill with filling. Use the remaining cheese and sprinkle on the tops. Bake for 12-14 minutes until cheese is melted and starting to brown. I spooned the leftover stuffing mix around the squash because trust me you will want more! Garnish with fresh thyme sprigs and enjoy!