Preheat oven to 375 degrees F (190 degrees C). Lightly grease a baking sheet.
Whisk flour, muffin mix, brown sugar, baking powder, nutmeg, and salt together in a bowl. Cut butter into flour mixture using a pastry blender or fork until it resembles coarse crumbs.
Combine apple and dried cranberries together in a bowl; mix into flour mixture.
Beat half-and-half and egg together in a bowl until frothy; slowly stir into flour mixture using a rubber spatula until dough forms. Knead dough 4 to 5 times. Roll dough into a rectangle onto a lightly floured work surface using your hands. Cut rectangle in half diagonally and each half into 4 triangles, making 8 triangles. Arrange triangles on the prepared baking sheet.
Whisk egg white and confectioners' sugar together in a bowl; brush over each triangle.
Bake in the preheated oven until scones are golden brown, about 20 minutes.