Preheat oven to 450 F. Line a baking sheet with parchment paper. Season both squash halves with salt and pepper, drizzle with 1 tablespoon olive oil and place cut side down on baking sheet. Cover tightly with foil and roast for about 35 minutes or until tender when pierced with a paring knife.
Cook the wild rice blend according to package directions in chicken broth.
In the meantime, in a large frying pan, heat 2 tablespoons of olive oil over medium high heat. Add the shiitake mushrooms, onion, thyme, dried cranberries, and season with salt and pepper. Saute for about 8-10 minutes. Remove from heat.
When the rice is cooked, add to the mushroom mixture and combine.
When squash is cooked, remove from the oven and turn oven to broiler. Scoop out 2 tablespoons from each squash half and stir into the rice mushroom mixture. Adjust for taste with salt and pepper.
Spoon the rice mushroom mixture into the squash halves and top with grated Parmesan cheese. Broil for about 2 minutes or until cheese is melted.