In a small saucepan over medium heat, combine raspberries, granulated sugar, lemon zest, lemon juice, cinnamon, nutmeg, ginger, and salt. Cook, stirring occasionally, until mixture is thick and jamlike, about 30 minutes.
Meanwhile, in a small bowl, whisk egg with milk to blend and set aside. Put turbinado sugar in another small bowl.
Lightly flour a work surface and lay half of pastry on top. Use a 3-in. heart-shaped cookie cutter to cut hearts from pastry. Set on a rimmed baking sheet lined with parchment paper and chill while you cut hearts from remaining pastry. Reroll pastry scraps once and cut more hearts. (After that, the dough will begin to get too tough.)
Spread a scant 1 tbsp. raspberry filling onto each of half the hearts. With a small pastry brush or your finger, coat outer 1/2 in. or so of fruit-topped hearts with egg mixture. Using a small knife, cut a 3/4-in. heart in centers of remaining pastry hearts. These will be the tops of the pie hearts.
Gently stretch one of the pie-heart tops with your fingers. Place it over a fruit-topped heart and press edges together with your fingers to seal. Repeat with remaining hearts.
Set assembled hearts about 1 in. apart on two parchment-lined baking sheets. Lightly brush tops of hearts with egg mixture. Sprinkle generously with turbinado sugar. Chill pie hearts at least 20 minutes while oven preheats.
Preheat oven to 375°. Bake pie hearts until golden brown and bubbling, switching pan positions halfway through baking, 15 to 18 minutes total.
Remove from oven and cool in pans 10 minutes, then transfer to racks to cool completely.