Cut squash in half lengthwise; remove seeds and any fibrous material from center of squash. Cut squash into smaller pieces and place in a shallow baking dish; cover tightly. Bake at 350° for 1 hour and 15 minutes or until tender.
Remove squash from baking dish. Remove pulp from squash; discard skin. Mash pulp well using a fork. Drain thoroughly.
Combine mashed squash, eggs, 1/2 cup brown sugar, butter, vanilla, and pumpkin pie spice; mix well. Spoon mixture into a well-greased 2-quart casserole. Combine coconut and 3 tablespoons brown sugar; sprinkle evenly over top of casserole. Bake, uncovered, at 350° for 45 minutes.