Preheat oven to 400°.
Combine first 3 ingredients in a medium bowl, stirring well with a whisk. Place juice in another bowl. Working with 1 quince at a time, dip quince in juice, turning to coat; dredge quince in sugar mixture, turning to coat. Place quince, stem side up, in 8-inch square baking dish. Repeat procedure with remaining quinces, juice, and sugar mixture. Sprinkle quinces evenly with remaining sugar mixture. Pour cider in bottom of dish; place 1 teaspoon butter on top of each quince. Bake at 400° for 1 hour and 30 minutes or until quinces are golden brown and liquid is thick, basting every 30 minutes. Place 1 quince on each of 6 plates; drizzle quinces evenly with remaining syrup in pan.
Place cream in a medium bowl; beat with a mixer at medium speed until soft peaks form. Add powdered sugar, 1 tablespoon at a time; continue beating until stiff peaks form. Serve quinces warm with whipped cream. Garnish with freshly grated nutmeg, if desired.