Fried Apple Pie with Vanilla Bean Ice Cream and Apple-Brown Butter Caramel

1 recipe Apple Pie Filling, chilled, recipe follows

Vegetable oil , for frying

1 recipe Royal Icing, recipe follows

1 recipe Vanilla Bean Ice Cream, for serving, recipe follows, or your favorite vanilla ice cream

1 recipe Apple Brown Butter Sauce, recipe follows Pie Dough for Handpies:

2 

1/2 cups all-purpose flour

1 teaspoon sugar

1 teaspoon salt

6 ounces butter , diced

1/4 cup shortening , diced

1 tablespoon white vinegar

1/4 cup water , plus more if needed Apple Pie Filling:

3 apple s, small dice

2 teaspoons lemon juice

1 cup water

3/4 cup sugar

3 tablespoons cornstarch

1/2 teaspoon ground cinnamon

1/2 teaspoon salt

1/4 teaspoon ground nutmeg Royal Icing:

1 cup confectioners' sugar

2 tablespoons milk Real Vanilla Bean Ice Cream:

1 vanilla bean

2 cups whole milk

1 cup heavy cream

5 large egg s

1/2 cup sugar

1 teaspoon vanilla extract