Place squash and onion in a medium saucepan; add water to cover. Bring to a boil; reduce heat, and simmer, uncovered, 15 minutes or until squash is tender. Drain squash and onion; add carrot, water chestnuts, and pimiento.
Melt 2 tablespoons butter in a heavy saucepan over low heat; add flour, stirring until smooth. Cook, stirring constantly, 1 minute. Gradually add half-and-half, stirring constantly; cook over medium heat, stirring constantly, until mixture is thickened and bubbly. Stir in salt, peppers, nutmeg, and hot sauce. Gradually stir in sour cream, cheese, and egg.
Combine sauce mixture and vegetable mixture, stirring well. Spoon mixture into a lightly greased shallow 2-quart casserole. Combine stuffing mix and melted butter; sprinkle over squash mixture. Bake, uncovered, at 350° for 45 minutes or until thoroughly heated.