1. Preheat oven to 375 degree F and arrange rack in middle of oven; lightly brush a baking sheet with oil. Place squash, cut side down, on prepared sheet. Bake until just tender but not falling apart, about 25 minutes. Turn squash over and transfer, on sheet, to rack to cool.
2. Meanwhile, rinse lamb and pat dry. Heat oil in a large nonstick skillet over moderately high heat and brown lamb, seasoning with salt and pepper, turning occasionally, about 5 minutes. Drain in a colander set over a bowl, reserving skillet (discard fat in bowl).
3. Add butter, onions, parsnip, turnip, and thyme to skillet; cook over moderately high heat, stirring, until golden brown and softened, about 4 minutes. Sprinkle flour over vegetables and cook, stirring constantly, 1 minute. Add wine and simmer, stirring until evaporated, about 1 minute. Add broth and cook, stirring, until liquid is reduced and slightly thickened, about 4 minutes. Remove pan from heat and stir in lamb, for filling. (Can be made ahead. Cool and freeze in an airtight container up to 1 week. Reheat in a heavy saucepan over moderate heat, stirring, until hot, about 20 minutes.)
4. Scoop out squash from shells into a bowl, keeping shells intact. Mash squash with a fork; salt and pepper to taste.
5. Spoon filling into each squash shell and top with squash, spreading evenly. Bake until hot, about 15 minutes. Top with cheese. Makes 6 servings.