Place squash on a baking sheet and bake for 30 minutes or until tender. After allowing squash to cool, cut it in half lengthwise, seed, quarter and peel it. Then cut it into 1/2-inch cubes and set aside.
Increase oven temperature to 400 degrees.
In a medium saucepan over low heat, bring broth, water, and sage to a simmer without allowing it to come to a boil.
In a large nonstick skillet or wok, heat 1 teaspoon of the olive oil over medium-high heat and brown the sausage; set aside.
In the same skillet, saute onion in remaining olive oil over medium-high heat until tender.
Add the apple and garlic, and saute for two minutes.
Add the rice, and saute for an additional minute.
Stir in the sausage, squash, broth mixture, wine, chopped thyme, salt, and pepper, and cook for 5 minutes, stirring occasionally.
Place the casserole mixture in a 13 x 9-inch baking dish coated with cooking spray.
Bake at 400 degrees for 30 minutes.
Remove casserole from oven, stir mixture gently, and sprinkle with cheese.
Return to oven and bake for an additional five minutes, or until cheese is melted and bubbly.