Rinse squash; cut in half lengthwise and scoop out seeds. Place halves cut side down in a 12- by 17-inch baking pan. Peel, halve, and core apples; add to pan, along with 1/4 cup water.
Bake in a 400° regular or convection oven until squash and apples are tender when pierced, about 45 minutes. When cool enough to handle, scoop flesh of squash from peels; discard peels.
In a blender or food processor, in batches if necessary, whirl squash, apples, and broth until smooth. Pour purée into a 3- to 4-quart pan. Add wine, cinnamon, nutmeg, ginger, and chili flakes. Bring to a simmer over medium-high heat; reduce heat and simmer, stirring occasionally, to blend flavors, about 15 minutes. Add salt and pepper to taste.
Ladle soup into wide bowls and garnish with chives.