In the bowl of a food processor, combine flour, 1/2 cup sugar and salt. Pulse several times to combine.
Add 1 pound butter. Pulse just until butter is in small pieces.
Add ice water in small amounts, pulsing briefly with each addition. Add just enough water to make a crumbly mass, not a solid ball.
Remove dough from processor and press together. Divide into 3 portions.
Shape each portion into a round. Wrap each in plastic wrap. Place in refrigerate and cool for at least 1 hour, up to 2 days ahead.
Melt remaining 10 tablespoons butter in a large skillet.
Add remaining 1 1/3 cups sugar. Cook over medium-high heat until mixture turns light brown, about 5 minutes, stirring constantly.
Add apples. Reduce heat to medium. Cook until apples are just tender, about 5 minutes.
Stir in cinnamon, nutmeg and dissolved cornstarch. Cook 1 minute or until mixture thickens.
Remove from heat and allow to cool.
When ready to bake, preheat oven to 350°F.
Line two rimmed baking sheets with parchment paper.
Remove one portion of dough from refrigerator. Divide into three pieces.
Roll each portion into a 9-inch circle.
Do the same with the remaining 2 dough portions. (You will have nine 9-inch circles of dough.)
Divide filling into nine portions.
Place 1 portion in center of a pastry circle. Fold in sides of pastry to cover filling, leaving a 4-inch opening in the center with filling exposed.
Transfer crostada onto prepared baking sheet.
Repeat process with remaining dough and filling.
Brush crostadas with cream. Sprinkle with large crystal sugar.
Place in preheated oven. Bake 35 minutes or until crostadas have browned.
Remove from oven and allow to cool slightly before serving.
Serve with ice cream and garnish with mint.