In a small bowl, combine currants, walnuts and 1/2 tsp. cinnamon. Stir in 3 Tbsp. honey.

Peel apples and cut each in half lengthwise.

Trim away stem and blossom ends. Scoop out core from each half with a melon baller, making a wide hole for filling.

Divide honey mixture evenly between apple centers.

Divide pie dough into 4 balls. Roll each ball into a 6-inch circle about 1/4-inch thick.

Lay 1 piece of dough over each apple half with filling-side up. Tuck and wrap dough around each apple half. Trim dough to fit. Pinch the edges of dough underneath apples to seal entirely.

Combine 1 Tbsp. honey with 1 tsp. steaming hot water. Stir until honey dissolves. Brush mixture over tops of turnovers; dust with additional cinnamon.

Transfer turnovers to an ungreased baking sheet. Bake at 375°F for about 35 minutes, until turnovers art golden.

Remove from oven and drizzle with remaining 2 Tbsp. honey.

Serve warm or at room temperature.