In a large skillet with a lid, heat 2 tablespoons butter over medium; add onion, and season with salt and pepper. Cook, stirring occasionally, until softened, 3 to 5 minutes.
Add squash, apples, and 1 cup water. Cover, and simmer until squash is tender and most of the liquid has evaporated, 15 to 20 minutes. (If skillet becomes dry, add a little water; if liquid has not evaporated by the time squash is cooked, drain.)
Transfer squash mixture to a food processor. Add remaining butter; process until smooth. Season with salt and pepper; serve. (If serving later, gently reheat in a medium saucepan over low.)