Remove a slice from the stem end of the squash. Scoop out the pulp, leaving a 1/4 inch shell around outside. Repeat the procedure with the remaining squash.
Chop up the squash pulp that you have scooped out. Sauté the mushrooms, green onions and squash pulp in 1/4 cup of butter in a large skillet, for 8 minutes. Add the cooked rice and the broth. Add pepper to season to your taste. Mix it all together well.
Place the squash shells in an baking dish. Spoon the rice mixture into the shells. Dot with the remaining butter. Pour water 1/2 inch deep into the baking dish. Cover and bake at 350°F for 50 minutes or until tender. Sprinkle with paprika to serve.