Sprinkle with brown sugar and cinnamon; season with salt and pepper.
Drizzle with syrup; dot with 1 tablespoon butter.
Pour 1/2 cup water into bottom of pan.
Bake until squash is tender, about 1 hour. Cool completely.
Scoop out squash into bowl. Mash.
Transfer 3/4 cup squash to medium bowl (reserve remaining squash for another use).
Mix in ricotta, 1/4 cup grated Parmesan, 2 tablespoons parsley and thyme. Season with salt and pepper.
Place wrappers on work surface.
Place 1 level tablespoon filling in center of each.
Brush edges with water; fold each in half, pressing edges to seal. (Ravioli can be made 4 hours ahead. Arrange in single layer on foil-lined baking sheets dusted with flour. Cover and refrigerate.)
Melt 2 tablespoons butter in large pan over medium heat.
Add shallots; sauté 1 minute.
Add stock and cider; simmer 8 minutes.
Add 1 tablespoon parsley. Season with salt and pepper.
Working in batches, cook ravioli in pot of boiling salted water until just tender, about 1 minute. Using slotted spoon, divide ravioli among shallow soup bowls. Bring cider broth to simmer; ladle over ravioli. Top with shaved Parmesan.