Rub quinces thoroughly with a damp cloth.
Cut each quince into 4 pieces and remove stems and cores.
Place in a large saucepan with water; cook over low heat 45 minutes.
Press cooked quinces through a strainer.
Measure pulp into cups and make a note of the amount obtained.
Put pulp into a large bowl; add orange and lemon peel, cinnamon and cherry brandy.
Cover and let stand overnight.
Add 1-1/4 cups (300 g) sugar to mixture for every 1-3/4 cups (500 g) of pulp; mix well.
Heat pulp mixture in a large saucepan over medium heat until sugar has dissolved.
Continue to cook over low heat until mixture reaches a thick consistency and comes away from sides of pan.
Stir occasionally while cooking.
Preheat oven to 225°F (105°C).
Line two 7x11-inch (18x28-cm) cake pans with waxed paper; grease paper well.
Stir candied peel into quince pulp.
Divide mixture between 2 prepared pans; smooth the surface.
Dry out 3 to 4 hours in oven with oven door slightly open.
Cool completely then cut into diamond shapes; coat in remaining sugar.