Preheat oven to 375 degrees.
Season squash with salt and pepper. Place cut side down in a 9-by-13-inch baking dish. Add 3/4 cup water and roast until tender when pierced with a knife, about 45 minutes. Let cool.
Meanwhile, on a rimmed baking sheet, toss shrimp with 1 teaspoon oil; season with salt and pepper. Roast until cooked through, 8 to 10 minutes.
Scoop out seeds from squash and discard. With a fork, scrape flesh into a large bowl. Add shrimp and any cooking juices, lemon juice, and 1 tablespoon oil; toss to combine.
Season with salt and pepper, top with parsley and serve with lemon wedges.